19.1.10 problem 10

Internal problem ID [3524]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:40:31 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+32 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 51

dsolve(diff(y(x),x)=(x^2*y(x)-32)/(16-x^2) + 32,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-1440 \,{\mathrm e}^{-x -4} \left (x +4\right )^{2} \operatorname {Ei}_{1}\left (-x -4\right )+c_{1} \left (x +4\right )^{2} {\mathrm e}^{-x}+32 x^{2}-1696 x -7168}{\left (x -4\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.264 (sec). Leaf size: 56

DSolve[D[y[x],x]==(x^2*y[x]-32)/(16-x^2) + 32,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-x-4} \left (1440 (x+4)^2 \operatorname {ExpIntegralEi}(x+4)+e^4 \left (32 e^x \left (x^2-53 x-224\right )+c_1 (x+4)^2\right )\right )}{(x-4)^2} \]