29.8.17 problem 222

Internal problem ID [4822]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 222
Date solved : Monday, January 27, 2025 at 09:41:29 AM
CAS classification : [_linear]

\begin{align*} \left (1+x \right ) y^{\prime }&=\left (1+x \right )^{4}+2 y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve((1+x)*diff(y(x),x) = (1+x)^4+2*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 22

DSolve[(1+x) D[y[x],x]==(1+x)^4+2 y[x],y[x],x,IncludeSingularSolutions -> True]
 

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