Internal problem ID [15196]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 338.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]]
\[ \boxed {2 y^{\prime \prime }-\frac {y^{\prime }}{x}-\frac {x^{2}}{y^{\prime }}=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = \frac {\sqrt {2}}{5}, y^{\prime }\left (1\right ) = \frac {\sqrt {2}}{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 12
dsolve([2*diff(y(x),x$2)=diff(y(x),x)/x+x^2/diff(y(x),x),y(1) = 1/5*2^(1/2), D(y)(1) = 1/2*2^(1/2)],y(x), singsol=all)
\[ y = \frac {\sqrt {2}\, x^{\frac {5}{2}}}{5} \]
✓ Solution by Mathematica
Time used: 0.12 (sec). Leaf size: 26
DSolve[{2*y''[x]==y'[x]/x+x^2/y'[x],{y[1]==Sqrt[2]/5,y'[1]==Sqrt[2]/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} \sqrt {2} x^{3/2} \sqrt {x^2} \]