74.6.25 problem 26

Internal problem ID [16048]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 08:30:35 AM
CAS classification : [_exact]

\begin{align*} 2 t \sin \left (y\right )-2 t y \sin \left (t^{2}\right )+\left (t^{2} \cos \left (y\right )+\cos \left (t^{2}\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.193 (sec). Leaf size: 19

dsolve((2*t*sin(y(t))-2*t*y(t)*sin(t^2))+(t^2*cos(y(t))+cos(t^2) )*diff(y(t),t)=0,y(t), singsol=all)
 

\[ y \cos \left (t^{2}\right )+t^{2} \sin \left (y\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.372 (sec). Leaf size: 76

DSolve[(2*t*Sin[y[t]]-2*t*y[t]*Sin[t^2])+(t^2*Cos[y[t]]+Cos[t^2] )*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(t)}\left (\cos (K[2]) t^2+\cos \left (t^2\right )-\int _1^t-2 K[1] \left (\sin \left (K[1]^2\right )-\cos (K[2])\right )dK[1]\right )dK[2]+\int _1^t-2 K[1] \left (\sin \left (K[1]^2\right ) y(t)-\sin (y(t))\right )dK[1]=c_1,y(t)\right ] \]