40.14.15 problem 36

Internal problem ID [6786]
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
Date solved : Monday, January 27, 2025 at 02:30:27 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.016 (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 \cos \left (x \right ) c_2 -2 \sin \left (x \right ) c_1} \\ y &= -1+\sqrt {1+2 \cos \left (x \right ) c_2 -2 \sin \left (x \right ) c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 25.020 (sec). Leaf size: 5629

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

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