Internal problem ID [14402]
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: 66.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.469 (sec). Leaf size: 23
dsolve([y(t)*sin(t/y(t))-(t+t*sin(t/y(t)))*diff(y(t),t)=0,y(1) = 2],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z} -\operatorname {Si}\left (t \,{\mathrm e}^{-\textit {\_Z}}\right )-\ln \left (2\right )+\operatorname {Si}\left (\frac {1}{2}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 34
DSolve[{y[t]*Sin[t/y[t]]-(t+t*Sin[t/y[t]])*y'[t]==0,{y[1]==2}},y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (\frac {y(t)}{t}\right )-\text {Si}\left (\frac {t}{y(t)}\right )=-\text {Si}\left (\frac {1}{2}\right )-\log (t)+\log (2),y(t)\right ] \]