40.4.21 problem 23 (a)

Internal problem ID [6661]
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 : 23 (a)
Date solved : Monday, January 27, 2025 at 02:18:23 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{2} \cos \left (y\right ) y^{\prime }&=2 x \sin \left (y\right )-1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 20

dsolve(x^2*cos(y(x))*diff(y(x),x)=2*x*sin(y(x))-1,y(x), singsol=all)
 

\[ y = -\arcsin \left (\frac {3 c_1 \,x^{3}-1}{3 x}\right ) \]

✓ Solution by Mathematica

Time used: 10.037 (sec). Leaf size: 21

DSolve[x^2*Cos[y[x]]*D[y[x],x]==2*x*Sin[y[x]]-1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arcsin \left (\frac {1}{3 x}+2 c_1 x^2\right ) \]