Internal problem ID [14892]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 73.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {t \left (y^{\prime \prime } y+{y^{\prime }}^{2}\right )+y^{\prime } y=1} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 11
dsolve([t*(diff(y(t),t$2)*y(t)+diff(y(t),t)^2)+diff(y(t),t)*y(t)=1,y(1) = 1, D(y)(1) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \sqrt {2 t -1} \]
✓ Solution by Mathematica
Time used: 0.371 (sec). Leaf size: 14
DSolve[{t*(y''[t]*y[t]+y'[t]^2)+y'[t]*y[t]==1,{y[1]==1,y'[1]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \sqrt {2 t-1} \]