Internal problem ID [5435]
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: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {y y^{\prime \prime }-{y^{\prime }}^{2} \left (1-y^{\prime } \cos \left (y\right )+y y^{\prime } \sin \left (y\right )\right )=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 22
dsolve(y(x)*diff(y(x),x$2)=diff(y(x),x)^2*(1-diff(y(x),x)*cos(y(x))+y(x)*diff(y(x),x)*sin(y(x)) ),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= c_{1} \\ \sin \left (y \left (x \right )\right )+c_{1} \ln \left (y \left (x \right )\right )-x -c_{2} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.425 (sec). Leaf size: 63
DSolve[y[x]*y''[x]==y'[x]^2*(1-y'[x]*Cos[y[x]]+y[x]*y'[x]*Sin[y[x]] ),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}[\sin (\text {$\#$1})+c_1 \log (\text {$\#$1})\&][x+c_2] \\ y(x)\to \text {InverseFunction}[\sin (\text {$\#$1})-c_1 \log (\text {$\#$1})\&][x+c_2] \\ y(x)\to \text {InverseFunction}[\sin (\text {$\#$1})+c_1 \log (\text {$\#$1})\&][x+c_2] \\ \end{align*}