32.6.22 problem Exercise 12.22, page 103

Internal problem ID [5887]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.22, page 103
Date solved : Monday, January 27, 2025 at 01:24:38 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (y^{2}+a \sin \left (x \right )\right ) y^{\prime }&=\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 43

dsolve((y(x)^2+a*sin(x))*diff(y(x),x)=cos(x),y(x), singsol=all)
 

\[ \frac {\left (-a^{3} \sin \left (x \right )-a^{2} y \left (x \right )^{2}-2 a y \left (x \right )-2\right ) {\mathrm e}^{-a y \left (x \right )}+c_{1} a^{3}}{a^{3}} = 0 \]

✓ Solution by Mathematica

Time used: 0.199 (sec). Leaf size: 45

DSolve[(y[x]^2+a*Sin[x])*D[y[x],x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\sin (x) \left (-e^{-a y(x)}\right )-\frac {e^{-a y(x)} \left (a^2 y(x)^2+2 a y(x)+2\right )}{a^3}=c_1,y(x)\right ] \]