Internal problem ID [2010]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (x^{2}-1\right ) y^{\prime }+4 y=-\left (x^{2}-1\right )^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = -6] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {\left (-\frac {x^{3}}{3}+2 x^{2}-7 x +8 \ln \left (x +1\right )-6\right ) \left (x +1\right )^{4}}{\left (x^{2}-1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 38
DSolve[{(x^2-1)*y'[x]+(x^2-1)^2+4*y[x]==0,{y[0]==-6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {(x+1)^2 \left (x^3-6 x^2+21 x-24 \log (x+1)+18\right )}{3 (x-1)^2} \]