12.1 problem 320

Internal problem ID [3068]

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]

Solve \begin {gather*} \boxed {\left (x +a \right )^{2} y^{\prime }-2 \left (x +a \right ) \left (b +y\right )=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 15

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

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

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*}