Internal problem ID [2244]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 24, page 109
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+3 y=\sin \left (x \right ) x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=x^2*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{3 x}+\frac {\left (25 x^{2}+55 x +28\right ) \cos \left (x \right )}{125}+\frac {\left (25 x^{2}-20 x -67\right ) \sin \left (x \right )}{250}+{\mathrm e}^{x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 52
DSolve[y''[x]-4*y'[x]+3*y[x]==x^2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{250} \left (\left (25 x^2-20 x-67\right ) \sin (x)+2 \left (25 x^2+55 x+28\right ) \cos (x)\right )+c_1 e^x+c_2 e^{3 x} \]