28.1.66 problem 68

Internal problem ID [4372]
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
Date solved : Monday, January 27, 2025 at 09:09:25 AM
CAS classification : [_linear]

\begin{align*} \left (1+x \right ) y^{\prime }-y&=x \left (1+x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

dsolve((1+x)*diff(y(x),x)-y(x)=x*(1+x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (x^{2}+2 c_{1} \right ) \left (x +1\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 20

DSolve[(1+x)*D[y[x],x]-y[x]==x*(1+x)^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} (x+1) \left (x^2+2 c_1\right ) \]