Internal problem ID [2072]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {\frac {2 y^{3}-2 y^{3} x^{2}-x +x y^{2} \ln \left (y\right )}{x y^{2}}+\frac {\left (2 \ln \left (x \right ) y^{3}-y^{3} x^{2}+2 x +x y^{2}\right ) y^{\prime }}{y^{3}}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.532 (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)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-x^{2} {\mathrm e}^{3 \textit {\_Z}}+2 \ln \left (x \right ) {\mathrm e}^{3 \textit {\_Z}}+\textit {\_Z} x \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{2 \textit {\_Z}}-x \right )} \]
✓ Solution by Mathematica
Time used: 0.685 (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)*y'[x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2 y(x)+\frac {x}{y(x)^2}-x \log (y(x))-2 y(x) \log (x)=2,y(x)\right ] \]