Internal problem ID [13196]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.7 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }+2 {y^{\prime }}^{2}-3 y y^{\prime }=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = {\frac {3}{4}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 14
dsolve([y(x)*diff(y(x),x$2)+2*diff(y(x),x)^2=3*y(x)*diff(y(x),x),y(0) = 2, D(y)(0) = 3/4],y(x), singsol=all)
\[ y \left (x \right ) = \left (3 \,{\mathrm e}^{3 x}+5\right )^{\frac {1}{3}} \]
✓ Solution by Mathematica
Time used: 1.151 (sec). Leaf size: 18
DSolve[{y[x]*y''[x]+2*y'[x]^2==3*y[x]*y'[x],{y[0]==2,y'[0]==3/4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt [3]{3 e^{3 x}+5} \]