29.8.26 problem 231

Internal problem ID [4831]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 231
Date solved : Monday, January 27, 2025 at 09:41:48 AM
CAS classification : [_linear]

\begin{align*} \left (x +a \right ) y^{\prime }&=2 \left (x +a \right )^{5}+3 y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve((a+x)*diff(y(x),x) = 2*(a+x)^5+3*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (2 a x +x^{2}+c_{1} \right ) \left (x +a \right )^{3} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 21

DSolve[(a+x) D[y[x],x]==2(a+x)^5+3 y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (a+x)^3 \left (2 a x+x^2+c_1\right ) \]