Internal problem ID [2044]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.4, page 36
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y x^{2}-32}{-x^{2}+16}-32=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 77
dsolve(diff(y(x),x)=(x^2*y(x)-32)/(16-x^2) + 32,y(x), singsol=all)
\[ y \relax (x ) = \left (32 \,{\mathrm e}^{x}-1440 \,{\mathrm e}^{-4} \expIntegral \left (1, -4-x \right )+\frac {128 \,{\mathrm e}^{x}}{\left (x +4\right )^{2}}-\frac {1952 \,{\mathrm e}^{x}}{x +4}+c_{1}\right ) \left (\frac {{\mathrm e}^{-x} x^{2}}{\left (x -4\right )^{2}}+\frac {8 \,{\mathrm e}^{-x} x}{\left (x -4\right )^{2}}+\frac {16 \,{\mathrm e}^{-x}}{\left (x -4\right )^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.15 (sec). Leaf size: 52
DSolve[y'[x]==(x^2*y[x]-32)/(16-x^2) + 32,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x-4} \left (32 e^{x+4} ((x-53) x-224)+(x+4)^2 \left (1440 \text {Ei}(x+4)+e^4 c_1\right )\right )}{(x-4)^2} \\ \end{align*}