Internal problem ID [2553]
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]
\[ \boxed {y^{\prime }-\frac {y x^{2}-32}{-x^{2}+16}=32} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 77
dsolve(diff(y(x),x)=(x^2*y(x)-32)/(16-x^2) + 32,y(x), singsol=all)
\[ y \left (x \right ) = \left (32 \,{\mathrm e}^{x}-1440 \,{\mathrm e}^{-4} \operatorname {Ei}_{1}\left (-x -4\right )+\frac {128 \,{\mathrm e}^{x}}{\left (x +4\right )^{2}}-\frac {1952 \,{\mathrm e}^{x}}{x +4}+c_{1} \right ) \left (\frac {{\mathrm e}^{-x} x^{2}}{\left (x -4\right )^{2}}+\frac {8 \,{\mathrm e}^{-x} x}{\left (x -4\right )^{2}}+\frac {16 \,{\mathrm e}^{-x}}{\left (x -4\right )^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 56
DSolve[y'[x]==(x^2*y[x]-32)/(16-x^2) + 32,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x-4} \left (1440 (x+4)^2 \operatorname {ExpIntegralEi}(x+4)+e^4 \left (32 e^x \left (x^2-53 x-224\right )+c_1 (x+4)^2\right )\right )}{(x-4)^2} \]