29.12.1 problem 320

Internal problem ID [4920]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 320
Date solved : Monday, January 27, 2025 at 09:50:39 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 24

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

\begin{align*} y(x)\to -b+c_1 (a+x)^2 \\ y(x)\to -b \\ \end{align*}