74.6.26 problem 27

Internal problem ID [16049]
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 : 27
Date solved : Tuesday, January 28, 2025 at 08:31:11 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _exact]

\begin{align*} \left (3+t \right ) \cos \left (t +y\right )+\sin \left (t +y\right )+\left (3+t \right ) \cos \left (t +y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 16

dsolve(( (3+t)*cos(t+y(t))+sin(t+y(t)) )+( (3+t)*cos(t+y(t)) )*diff(y(t),t)=0,y(t), singsol=all)
 

\[ y = -t +\arcsin \left (\frac {c_{1}}{3+t}\right ) \]

✓ Solution by Mathematica

Time used: 0.228 (sec). Leaf size: 104

DSolve[( (3+t)*Cos[t+y[t]]+Sin[t+y[t]] )+( (3+t)*Cos[t+y[t]] )*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^t(\cos (K[1]+y(t)) K[1]+\cos (K[1]+y(t)) (\tan (K[1]+y(t))+3))dK[1]+\int _1^{y(t)}\left (t \cos (t+K[2])+3 \cos (t+K[2])-\int _1^t(\sec (K[1]+K[2])-K[1] \sin (K[1]+K[2])-\sin (K[1]+K[2]) (\tan (K[1]+K[2])+3))dK[1]\right )dK[2]=c_1,y(t)\right ] \]