Internal problem ID [6101]
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: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime }-y^{\prime } \left (y^{\prime }+x^{3}\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2, y^{\prime }\relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.097 (sec). Leaf size: 25
dsolve([x^4*diff(y(x),x$2)=diff(y(x),x)*(diff(y(x),x)+x^3),y(1) = 2, D(y)(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = x^{2}-\ln \left (-x^{2}-1\right )+1+\ln \relax (2)+i \pi \]
✓ Solution by Mathematica
Time used: 0.883 (sec). Leaf size: 20
DSolve[{x^4*y''[x]==y'[x]*(y'[x]+x^3),{y[1]==2,y'[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2-\log \left (x^2+1\right )+1+\log (2) \\ \end{align*}