11.3 problem 294

Internal problem ID [3042]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 11
Problem number: 294.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }-\left (2 b x +a \right ) y=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 18

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

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

Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 26

DSolve[(1+x^2)y'[x]==(a+2 b x)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \left (x^2+1\right )^b e^{a \text {ArcTan}(x)} \\ y(x)\to 0 \\ \end{align*}