Internal problem ID [5310]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary
problems. Page 39
Problem number: 19 (o).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right )=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 54
dsolve(2*diff(x(y),y)-x(y)/y+x(y)^3*cos(y)=0,x(y), singsol=all)
\begin{align*} x \left (y \right ) = \frac {\sqrt {\left (\cos \left (y \right )+y \sin \left (y \right )+c_{1} \right ) y}}{\cos \left (y \right )+y \sin \left (y \right )+c_{1}} x \left (y \right ) = -\frac {\sqrt {\left (\cos \left (y \right )+y \sin \left (y \right )+c_{1} \right ) y}}{\cos \left (y \right )+y \sin \left (y \right )+c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.261 (sec). Leaf size: 53
DSolve[2*x'[y]-x[y]/y+x[y]^3*Cos[y]==0,x[y],y,IncludeSingularSolutions -> True]
\begin{align*} x(y)\to -\frac {\sqrt {y}}{\sqrt {y \sin (y)+\cos (y)+c_1}} x(y)\to \frac {\sqrt {y}}{\sqrt {y \sin (y)+\cos (y)+c_1}} x(y)\to 0 \end{align*}