40.4.13 problem 19 (o)

Internal problem ID [6653]
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)
Date solved : Monday, January 27, 2025 at 02:17:03 PM
CAS classification : [_Bernoulli]

\begin{align*} 2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (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: 0.276 (sec). Leaf size: 53

DSolve[2*D[x[y],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*}