Internal problem ID [5439]
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: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {\left (2 y+x \right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime }=2} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 49
dsolve((x+2*y(x))*diff(y(x),x$2)+2*diff(y(x),x)^2+2*diff(y(x),x)=2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {x}{2}-\frac {\sqrt {-4 c_{1} x +5 x^{2}+4 c_{2}}}{2} \\ y \left (x \right ) &= -\frac {x}{2}+\frac {\sqrt {-4 c_{1} x +5 x^{2}+4 c_{2}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.645 (sec). Leaf size: 77
DSolve[(x+2*y[x])*y''[x]+2*y'[x]^2+2*y'[x]==2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} x \left (1+\sqrt {\frac {1}{x^2}} \sqrt {5 x^2+4 c_2 x+4 c_1}\right ) \\ y(x)\to \frac {1}{2} x \left (-1+\sqrt {\frac {1}{x^2}} \sqrt {5 x^2+4 c_2 x+4 c_1}\right ) \\ \end{align*}