Internal problem ID [6836]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing.
EXERCISES Page 324
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {y^{\prime \prime }-x {y^{\prime }}^{2}=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 10
dsolve([diff(y(x),x$2)=x*diff(y(x),x)^2,y(0) = 1, D(y)(0) = 1/2],y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {arctanh}\left (\frac {x}{2}\right )+1 \]
✓ Solution by Mathematica
Time used: 0.229 (sec). Leaf size: 13
DSolve[{y''[x]==x*(y'[x])^2,{y[0]==1,y'[0]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {arctanh}\left (\frac {x}{2}\right )+1 \]