PAGEPAGE16實(shí)驗(yàn)報(bào)告四代數(shù)方程求解1(+1)x+xsi=0在0附近的一個(gè)根：>>y=sym('(x+1)*exp(-x)+exp(x)*sin(x)'); %sym命令定義符號(hào)表達(dá)式>>x=solve(y,'x') %0的一個(gè)根x=-0.86508244315736795185621568221837或可用以下命令求解該方程以指定點(diǎn)為初始搜索點(diǎn)的數(shù)值解：>>y=inline('(x+1)*exp(-x)+exp(x)*sin(x)','x'); %inline命令定義>>x=fsolve(y,0) %1開始搜索方程的近似解x=-0.8651solve0fsolve點(diǎn)的變化，得到不同的解（如果方程有多個(gè)實(shí)數(shù)解。e3tsin(4t2)4e0.5tcos(2t)0.5的一個(gè)根；再用數(shù)值方法分別求該方程在-0.63附近的兩個(gè)根。y=sym('exp(-3*t)*sin(4*t+2)+4*exp(-0.5*t)*cos(2*t)-0.5');t=solve(y,'t')t=0.67374570500134756702960220427474y=inline('exp(-3*t).*sin(4*t+2)+4*exp(-0.5*t).*cos(2*t)-0.5','t');t=fsolve(y,0.6)t=0.6737y=inline('exp(-3*t).*sin(4*t+2)+4*exp(-0.5*t).*cos(2*t)-0.5','t');t=fsolve(y,3)t=2.59372、【示例】以下命令可求解非線性方程組x3y3x98xy20>>eq1=sym('x^3+y^3-x-98'); %定義第一個(gè)方程表達(dá)式>>eq2=sym('x+y-2'); %定義第二個(gè)方程表達(dá)式>>[x,y]=solve(eq1,eq2) %解方程組（用準(zhǔn)解析方法）x=13/12+1/12*2329^(1/2)13/12-1/12*2329^(1/2)y=11/12-1/12*2329^(1/2)11/12+1/12*2329^(1/2)或可用以下命令求解上述方程組以指定點(diǎn)為初始搜索點(diǎn)的數(shù)值解：>>f=inline('[x(1)^3+x(2)^3-x(1)-98;x(1)+x(2)-2]','x'); %inline命令定義方程組>>x=fsolve(f,[1;1]) %用數(shù)值方法從初始點(diǎn)(1,1)開始搜索方程組的一個(gè)近似解x=-2.93834.9383【要求】仿照示例，求解x22x10（1）x33x25x3和方程組x3z4yz1x33x25x3（1）y=sym('x^3-3.*x^2+5*x');x=solve(y,'x')x=1.1.+1.4142135623730950488016887242097*i1.-1.4142135623730950488016887242097*i（2）y=inline('x^3-3.*x^2+5*x-3','x');x=fsolve(y,0)x=1.0000x22x10x3z4yz1（1）eq1=sym('x^2+2*x+1');eq2=sym('x+3*z-4');eq3=sym('y*z+1');[x,y,z]=solve(eq1,eq2,eq3)x=-1y=-3/5z=5/3（2）f=inline('[x(1)^2+2*x(1)+1;x(1)+3*x(3)-4;x(2)*x(3)+1]','x');x=fsolve(f,[1;1;1])x=-0.9979-0.60031.6660（2）方程組x2+y=0,ex+siny=0在[-5,5]內(nèi)的所有根。>>ezplot('-x^2',[-5,5])>>holdon>>ezplot('asin(-exp(x))',[-5,5])

asin(-exp(x))0-0.2-0.4-0.6-0.8-1-5 -4 -3 -2 -1 0 1 2 3 4 5xf=inline('[x(1)^2+x(2);exp(x(1))+sin(x(2))]','x');x=fsolve(f,[-0.7,-0.5])x=-0.7150-0.51122x

3x2

2x 84x3

5x2

2x x 23 4

。計(jì)算A*x，即可驗(yàn)證求解結(jié)果。3xx1 2

xx 73 44xx1 2

2x2x 123 4A=[2-302;1521;3-11-1;4122]; %定義方程組的系數(shù)矩陣B=[82712] %定義方程組的常數(shù)項(xiàng)向量x=A\B % A\BAx=3.00000.0000-1.00001.0000

24

16

5x 8【要求】執(zhí)行以上命令，并仿照示例，解線性方程組3x 2

127x3

2 31011x1

7x2

3x3

31A=[24165;03-27;117-3];B=[81031]';x=A\Bx= 19.4087-27.5410-3.4305實(shí)驗(yàn)報(bào)告五微分方程求解一、解析方法（dsolve命令）【示例】1、以下命令可求微分方程dx

y2的通解：x>>y=dsolve('Dy=y^2/x','x') %Dyy的一階導(dǎo)，x為自變量y=-1/(log(x)-C1)2dx

exy

x2e

x

0的特解：>>y=dsolve('Dy=exp(x-y)+x^2*exp(-y)','y(0)=0','x')y=log(exp(x)+1/3*x^3)3、以下命令可求微分方程組dt

y,dt

xt

t

1,

t

2下的特解：>>[x,y]=dsolve('Dy=-x+t','x(0)=1,y(0)=2','t') %、y為自變量4、以下命令可求二階微分方程yyx1在初始條件y1,y1的通解：x0 x0>>y=dsolve('D2y-Dy+x=1','y(0)=1,Dy(0)=1','x') %D2yy為自變量y=1/2*x^2+exp(x)1、執(zhí)行以上命令，并仿照示例，解微分方程xy2dx(1x2dy0，并求它滿足初始條件y1的特解。x0y=dsolve('Dy=(x*y^2)/(1+x^2)','x')y=-2/(log(1+x^2)-2*C1)y=dsolve('Dy=(x*y^2)/(1+x^2)','y(0)=1','x')y=-2/(log(1+x^2)-2)2y4y13ye2xx1)sinx的通解。y=dsolve('D2y+4*Dy+13*y=exp(-2*x)*(x+1)*sin(x)','x')y=exp(-2*x)*sin(3*x)*C2+exp(-2*x)*cos(3*x)*C1+1/32*exp(-2*x)*(-cos(x)+4*sin(x)*x+4*sin(x))二、數(shù)值方法（ode命令）dxy1、【示例】以下命令可求微分方程組dtdy(1x2)ydt先在Editor窗口中編寫M文件：

當(dāng)自變量在[0,30]之間的數(shù)值解。functiondz=fun1(t,z) %fun1dz=zeros(2,1);dz(1)=z(2); %z(1)、xy，t為函數(shù)的自變量。dz(2)=(1-z(1)^2)*z(2)-z(1); dz(1)、dz(2)xy關(guān)于t的導(dǎo)數(shù)，必須單獨(dú)寫在左邊。然后在命令窗口中輸入命令>>[t,z]=ode45('fun1',[0,30],[1,0]);z %ode45名必須與前面的函數(shù)名一致，[0,30]表示自變量的取值范圍，[1,0]xy的初始值。z=1.000001.0000-0.00011.0000-0.00011.0000-0.00021.0000-0.00021.0000-0.00051.0000-0.00071.0000-0.00101.0000-0.00121.0000-0.00251.0000-0.00371.0000-0.00501.0000-0.00620.9999-0.01250.9998-0.01880.9997-0.02510.9995-0.03130.9980-0.06270.9956-0.09400.9921-0.12530.9877-0.15640.9546-0.29940.9009-0.44170.8265-0.58610.7306-0.73690.5989-0.91620.4367-1.11830.2400-1.34710.0052-1.5968-0.2703-1.8501-0.5812-2.0298-0.9096-2.0483-1.2240-1.8381-1.3582-1.6491-1.4763-1.4212-1.5759-1.1712-1.6560-0.9172-1.7170-0.6752-1.7602-0.4542-1.7874-0.2594-1.8008-0.0921-1.80170.0685-1.78970.2003-1.76700.3088-1.73570.3988-1.70150.4674-1.66230.5280-1.61860.5832-1.57070.6347-1.49390.7066-1.40900.7787-1.31560.8546-1.21310.9380-0.99351.1234-0.72581.3816-0.39221.73470.02532.16820.19672.32890.37982.47420.57292.58640.77252.64400.97392.62451.17032.51311.35432.30831.51972.02301.67051.65951.79061.27751.88020.91111.94150.58871.97480.35531.99290.16101.99850.00211.9939-0.12621.9813-0.22901.9622-0.31261.9376-0.38141.9086-0.43881.8786-0.48431.8458-0.52441.8105-0.56061.7730-0.59411.7155-0.63931.6539-0.68301.5881-0.72721.5182-0.77321.3914-0.85821.2502-0.95871.0918-1.08200.9117-1.23710.7679-1.37200.6077-1.53240.4283-1.72080.2265-1.93640.0000-2.1722-0.2531-2.4058-0.5302-2.5952-0.8227-2.6786-1.0977-2.5930-1.3546-2.3399-1.5768-1.9513-1.7538-1.4759-1.8607-1.0817-1.9361-0.7254-1.9842-0.4238-2.0094-0.1811-2.0157-0.0524-2.01550.0568-2.00980.1492-1.99950.2272-1.98530.2935-1.96770.3501-1.94730.3989-1.92440.4414-1.89280.4875-1.85830.5280-1.82120.5644-1.78180.5981-1.72450.6413-1.66340.6834-1.59830.7260-1.52920.7706-1.40260.8540-1.26180.9529-1.10401.0743-0.92481.2273-0.78131.3608-0.62161.5199-0.44261.7072-0.24141.9222-0.01522.15860.23792.39470.51562.58930.80942.68001.08382.60371.34122.36071.56491.97971.74431.50791.85331.11361.93090.75481.98110.44922.00810.20222.01540.07132.0162-0.04012.0114-0.13432.0019-0.21411.9884-0.28181.9716-0.33971.9519-0.38951.9296-0.43281.8990-0.47961.8655-0.52051.8294-0.55711.7909-0.59081.7354-0.63361.6760-0.67501.6129-0.71661.5460-0.75981.4261-0.83831.2935-0.92991.1458-1.04100.9794-1.17900.8387-1.30630.6820-1.45870.5065-1.63960.3088-1.85010.0860-2.0859-0.1647-2.3307-0.4422-2.5469-0.7394-2.6726-1.0114-2.6415-1.2714-2.4485-1.5029-2.1068-1.6941-1.6558-1.8143-1.2607-1.9028-0.8890-1.9628-0.5635-1.9982-0.2955-2.0102-0.1499-2.0149-0.0257-2.01340.0795-2.00650.1684-1.99520.2436-1.98020.3076-1.96190.3623-1.94080.4096-1.91270.4580-1.88170.5001-1.84820.5375-1.81230.5715-1.76090.6138-1.70590.6539-1.64750.6935-1.58550.7339-1.48010.8023-1.36470.8796-1.23780.9703-1.09721.0796-0.95801.1975-0.80281.3403-0.62841.5131-0.43071.7195-0.20611.95910.05022.22280.33882.47620.65392.65180.92452.67021.18862.53301.42992.23751.63481.81311.76961.41461.87151.02551.94270.67511.98680.38212.00620.18662.01340.02612.0105-0.10431.9995-0.20961.9851-0.28291.9668-0.34481.9451-0.39751.9206-0.44301.8892-0.48881.8549-0.52901.8181-0.56521.7789-0.59871.7213-0.64231.6596-0.68491.5941-0.72791.5244-0.77301.3965-0.85761.2542-0.95811.0943-1.08180.9126-1.23800.7685-1.37290.6080-1.53360.4281-1.72240.2260-1.9384-0.0011-2.1747-0.2548-2.4086-0.5326-2.5979-0.8257-2.6802-1.1009-2.5925-1.3577-2.3372-1.5795-1.9469-1.7561-1.4707-1.8626-1.0762-1.9376-0.7202-1.9853-0.4191-2.0102-0.1771-2.0163-0.0489-2.01590.0599-2.01000.1518-1.99960.2295-1.98520.2955-1.96760.3519-1.94700.4004-1.92400.4427-1.89230.4888-1.85770.5292-1.82050.5655-1.78090.5991-1.72340.6424-1.66200.6845-1.59670.7272-1.52730.7719-1.39970.8560-1.25790.9558-1.09861.0787-0.91771.2337-0.77381.3681-0.61361.5282-0.43401.7164-0.23221.9321-0.00542.16850.24822.40340.52602.59480.81952.68041.09442.59711.35142.34661.57391.95981.75161.48531.85901.09091.93500.73371.98370.43092.00940.18702.01600.05772.0161-0.05212.0107-0.14492.0006-0.22351.9866-0.29011.9693-0.34711.9491-0.39611.9264-0.43881.8951-0.48511.8609-0.52571.8241-0.56211.7850-0.59581.7283-0.63881.6678-0.68071.6033-0.72291.5350-0.76701.4106-0.84871.2726-0.94501.1182-1.06290.9435-1.21060.8011-1.34190.6427-1.49840.4652-1.68330.2655-1.89650.0409-2.1324-0.2109-2.3716-0.4880-2.5743-0.7826-2.6783-1.0560-2.6198-1.3144-2.3963-1.5412-2.0303-1.7252-1.5661-1.8383-1.1719-1.9200-0.8084-1.9741-0.4953-2.0044-0.2402-2.0135-0.1052-2.01600.0100-2.01280.1078-2.00470.1907-1.99260.2612-1.97700.3213-1.95850.3731-1.93730.4180-1.90830.4659-1.87630.5076-1.84170.5448-1.80480.5787-1.76370.6121-1.72030.6442-1.67470.6757-1.62700.7073將結(jié)果用圖形表示>>x=z(:,1);y=z(:,2); plot(t,x,'r',t,y,'b');3210-1-2-30 5 10 15 20 25 30figure; plot(x,y)3210-1-2-3-2.5 -2 -1.5 -1 -0.