Internal problem ID [3576]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 320.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (a +x \right )^{2} y^{\prime }-2 \left (a +x \right ) \left (b +y\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (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: 0.05 (sec). Leaf size: 24
DSolve[(a+x)^2 y'[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*}