15.6.24 problem 24

Internal problem ID [2981]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 24
Date solved : Monday, January 27, 2025 at 07:05:28 AM
CAS classification : [_linear]

\begin{align*} \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right )^{2}+4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-6 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 38

dsolve([(x^2-1)*diff(y(x),x)+(x^2-1)^2+4*y(x)=0,y(0) = -6],y(x), singsol=all)
 

\[ y = \frac {\left (-\frac {x^{3}}{3}+2 x^{2}-7 x +8 \ln \left (x +1\right )-6\right ) \left (x +1\right )^{4}}{\left (x^{2}-1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 38

DSolve[{(x^2-1)*D[y[x],x]+(x^2-1)^2+4*y[x]==0,{y[0]==-6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {(x+1)^2 \left (x^3-6 x^2+21 x-24 \log (x+1)+18\right )}{3 (x-1)^2} \]