Internal problem ID [5443]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary
problems. Page 132
Problem number: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {2 \left (1+y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(2*(y(x)+1)*diff(y(x),x$2)+2*diff(y(x),x)^2+y(x)^2+2*y(x)=0,y(x), singsol=all)
\begin{align*} y = -1-\sqrt {1+2 c_{2} \cos \left (x \right )-2 c_{1} \sin \left (x \right )} y = -1+\sqrt {1+2 c_{2} \cos \left (x \right )-2 c_{1} \sin \left (x \right )} \end{align*}
✓ Solution by Mathematica
Time used: 24.469 (sec). Leaf size: 5629
DSolve[2*(y[x]+1)*y''[x]+2*y'[x]^2+y[x]^2+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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