Internal problem ID [2702]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 68.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime }-y-x \left (x +1\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 15
dsolve((1+x)*diff(y(x),x)-y(x)=x*(1+x)^2,y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {x^{2}}{2}+c_{1}\right ) \left (x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 20
DSolve[(1+x)*y'[x]-y[x]==x*(1+x)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} (x+1) \left (x^2+2 c_1\right ) \\ \end{align*}