83.8.30 problem 31

Internal problem ID [19156]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 01:10:30 PM
CAS classification : [`x=_G(y,y')`]

\begin{align*} y-x y^{\prime }+x^{2}+1+x^{2} \sin \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

dsolve(y(x)-x*diff(y(x),x)+(1+x^2)+x^2*sin(y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ x +\frac {-y \left (x \right )-1}{x}-\cos \left (y \left (x \right )\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.137 (sec). Leaf size: 25

DSolve[y[x]-x*D[y[x],x]+(1+x^2)+x^2*Sin[y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\frac {y(x)}{x}-\cos (y(x))+x-\frac {1}{x}=c_1,y(x)\right ] \]