常微分方程[img=243x26]1802e4d57c1aad8.png[/img]的解为:
A: exp(-x)*sin(3^(1/2)*x)*C2+exp(-x)*cos(3^(1/2)*x)*C1-1/4*cos(2*x),C1、C2为任意常数
B: exp(-2x)*cos(3^(1/2)*x)*C2+exp(-2x)*cos(3^(1/2)*x)*C1-1/4*sin(2*x),C1、C2为任意常数
C: exp(-3x)*sin(3^(1/2)*x)*C2+exp(-3x)*sin(3^(1/2)*x)*C1-1/4*sin(2*x),C1、C2为任意常数
D: exp(-4x)*sin(3^(1/2)*x)*C2-exp(-4x)*cos(3^(1/2)*x)*C1-1/4*cos(2*x),C1、C2为任意常数
A: exp(-x)*sin(3^(1/2)*x)*C2+exp(-x)*cos(3^(1/2)*x)*C1-1/4*cos(2*x),C1、C2为任意常数
B: exp(-2x)*cos(3^(1/2)*x)*C2+exp(-2x)*cos(3^(1/2)*x)*C1-1/4*sin(2*x),C1、C2为任意常数
C: exp(-3x)*sin(3^(1/2)*x)*C2+exp(-3x)*sin(3^(1/2)*x)*C1-1/4*sin(2*x),C1、C2为任意常数
D: exp(-4x)*sin(3^(1/2)*x)*C2-exp(-4x)*cos(3^(1/2)*x)*C1-1/4*cos(2*x),C1、C2为任意常数
举一反三
- 求微分方程[img=143x21]17da5f14490e50e.png[/img]的通解,实验命令为(). A: dsolve(D2y-2*Dy+5*y=sin(2*x),x)ans =exp(x)*sin(2*x)*C2+exp(x)*cos(2*x)*C1+1/17*sin(2*x)+4/17*cos(2*x) B: dsolve('D2y-2*Dy+5*y=sin(2*x)','x')ans =cos(2*x)*(sin(4*x)/17 - cos(4*x)/68 + 1/4) - sin(2*x)*(cos(4*x)/17 + sin(4*x)/68) + C1*cos(2*x)*exp(x) - C2*sin(2*x)*exp(x) C: dsolve(D2y-2*Dy+5*y=sin(2*x),'x','y')ans =exp(x)*sin(2*x)*C2+exp(x)*cos(2*x)*C1+1/17*sin(2*x)+4/17*cos(2*x)
- 求微分方程[img=364x55]17da65386dfd612.png[/img]的通解; ( ) A: - cos(2*x)*exp(x)*(x/4 - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x) B: (3*sin(2*x)*exp(x))/32 - (sin(6*x)*exp(x))/32 - cos(2*x)*exp(x)*(x/4 - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x) C: - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x) D: (sin(6*x)*exp(x))/32 - cos(2*x)*exp(x)*(x/4 - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x)
- 将函数\(f(x)=\sin^4 x\)展开成Fourier级数为 ____ . A: \(f(x) = \frac{3}{8}-\frac{1}{2}\cos 2x +\frac{1}{8}cos 4x\) B: \(f(x) = \frac{1}{4}-\frac{1}{2}\cos x +\frac{3}{8}cos 4x\) C: \(f(x) = \frac{1}{4}-\frac{1}{2}\sin 2x -\frac{3}{8}cos 4x\) D: \(f(x) = \frac{3}{8}-\frac{1}{2}\sin x -\frac{1}{8}cos 4x\)
- 求不定积分[img=132x48]17da6537fc8dad6.png[/img]; ( ) A: -(4*(cos(x/2)/2 + 2*sin(x/2)))/(17*exp(2*x)) B: (4*(sin(x/2)/2 + 2*sin(x/2)))/(17*exp(2*x)) C: (4*(cos(x/2)/2 + 2*sin(x/2)))/(17*exp(2*x)) D: (4*(cos(x/2)/2 + 2*cos(x/2)))/(17*exp(2*x))
- 求微分方程[img=372x60]17da65376dc1787.jpg[/img]的通解。 ( ) A: C26*exp(3*x) + (x*exp(3*x)*(x + 1)^2)/2 + C27*x*exp(3*x) - (x^2*exp(3*x)*(2*x + 3))/6 B: C26*exp(3*x) + C27*x*exp(3*x) - (x^2*exp(3*x)*(2*x + 3))/6 C: C26*exp(3*x) + (x*exp(3*x)*(x + 1)^2)/2 D: C27*x*exp(3*x) - (x^2*exp(3*x)*(2*x + 3))/6