Internal problem ID [13520]
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: 13.8 (iii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {y^{\prime \prime }+2 x {y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 11
dsolve([diff(y(x),x$2)=-2*x*diff(y(x),x)^2,y(1) = 0, D(y)(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {-1+x}{x} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y''[x]==-2*x*y'[x]^2,{y[1]==0,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
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