Internal problem ID [2051]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.6, page 50
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-4 y x -x^{7} \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x)-4*x*y(x)=x^7*sin(x),y(x), singsol=all)
\[ y \relax (x ) = \left (\sin \relax (x )-x \cos \relax (x )+c_{1}\right ) x^{4} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 19
DSolve[x^2*y'[x]-4*x*y[x]==x^7*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^4 (\sin (x)-x \cos (x)+c_1) \\ \end{align*}