75.7.4 problem 178

Internal problem ID [16797]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 7, Total differential equations. The integrating factor. Exercises page 61
Problem number : 178
Date solved : Tuesday, January 28, 2025 at 09:28:04 AM
CAS classification : [_exact]

\begin{align*} 3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.109 (sec). Leaf size: 24

dsolve((3*x^2*tan(y(x))-2*y(x)^3/x^3  )+( x^3*sec(y(x))^2+4*y(x)^3+ 3*y(x)^2/x^2 )*diff(y(x),x)=0,y(x), singsol=all)
 

\[ x^{3} \tan \left (y\right )+\frac {y^{3}}{x^{2}}+y^{4}+c_{1} = 0 \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(3*x^2*Tan[y[x]]-2*y[x]^3/x^3  )+( x^3*Sec[y[x]]^2+4*y[x]^3+ 3*y[x]^2/x^2 )*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved