15.8.40 problem 42

Internal problem ID [3043]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 42
Date solved : Monday, January 27, 2025 at 07:11:19 AM
CAS classification : [_exact]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 2.470 (sec). Leaf size: 40

dsolve([((2*y(x)^3-2*x^2*y(x)^3-x+x*y(x)^2*ln(y(x)))/(x*y(x)^2))+( (2*y(x)^3*ln(x)-x^2*y(x)^3+2*x+x*y(x)^2)/y(x)^3)*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (-x^{2} {\mathrm e}^{3 \textit {\_Z}}+2 \ln \left (x \right ) {\mathrm e}^{3 \textit {\_Z}}+\textit {\_Z} x \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{2 \textit {\_Z}}-x \right )} \]

✓ Solution by Mathematica

Time used: 0.774 (sec). Leaf size: 30

DSolve[{((2*y[x]^3-2*x^2*y[x]^3-x+x*y[x]^2*Log[y[x]])/(x*y[x]^2))+( (2*y[x]^3*Log[x]-x^2*y[x]^3+2*x+x*y[x]^2)/y[x]^3)*D[y[x],x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x^2 y(x)+\frac {x}{y(x)^2}-x \log (y(x))-2 y(x) \log (x)=2,y(x)\right ] \]