83.43.3 problem Ex 4 page 7

Internal problem ID [19511]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 4 page 7
Date solved : Tuesday, January 28, 2025 at 01:47:13 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

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

✓ Solution by Maple

Time used: 0.102 (sec). Leaf size: 34

dsolve((x^3+x*y(x)^2+a^2*y(x))+(y(x)^3+y(x)*x^2-a^2*x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \cot \left (\operatorname {RootOf}\left (2 c_{1} a^{2} \sin \left (\textit {\_Z} \right )^{2}-2 \textit {\_Z} \,a^{2} \sin \left (\textit {\_Z} \right )^{2}-x^{2}\right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.233 (sec). Leaf size: 33

DSolve[(x^3+x*y[x]^2+a^2*y[x])+(y[x]^3+y[x]*x^2-a^2*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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