Internal problem ID [14381]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{2} \sqrt {y^{2}+t^{2}}-t y \sqrt {y^{2}+t^{2}}\, y^{\prime }=-t^{3}} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 1.391 (sec). Leaf size: 22
dsolve([(t^3+y(t)^2*sqrt(t^2+y(t)^2))-(t*y(t)*sqrt(t^2+y(t)^2))*diff(y(t),t)=0,y(1) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \sqrt {-1+\left (3 \ln \left (t \right )+2 \sqrt {2}\right )^{\frac {2}{3}}}\, t \]
✓ Solution by Mathematica
Time used: 19.956 (sec). Leaf size: 80
DSolve[{(t^3+y[t]^2*Sqrt[t^2+y[t]^2])-(t*y[t]*Sqrt[t^2+y[t]^2])*y'[t]==0,{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sqrt {\sqrt [3]{-t^6 \left (-9 \log ^2(t)+12 \sqrt {2} \log (t)-8\right )}-t^2} \\ y(t)\to \sqrt {\sqrt [3]{t^6 \left (9 \log ^2(t)+12 \sqrt {2} \log (t)+8\right )}-t^2} \\ \end{align*}