Internal problem ID [13515]
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 (c).
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]]
\[ \boxed {3 y y^{\prime \prime }-2 {y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 9] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 11
dsolve([3*y(x)*diff(y(x),x$2)=2*diff(y(x),x)^2,y(1) = 1, D(y)(1) = 9],y(x), singsol=all)
\[ y \left (x \right ) = \left (3 x -2\right )^{3} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 12
DSolve[{3*y[x]*y''[x]==2*y'[x]^2,{y[1]==1,y'[1]==9}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (3 x-2)^3 \]