74.4.19 problem 19
Internal
problem
ID
[15912]
Book
:
INTRODUCTORY
DIFFERENTIAL
EQUATIONS.
Martha
L.
Abell,
James
P.
Braselton.
Fourth
edition
2014.
ElScAe.
2014
Section
:
Chapter
2.
First
Order
Equations.
Exercises
2.2,
page
39
Problem
number
:
19
Date
solved
:
Tuesday, January 28, 2025 at 08:19:13 AM
CAS
classification
:
[_separable]
\begin{align*} 3 \sin \left (t \right )-\sin \left (3 t \right )&=\left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime } \end{align*}
✓ Solution by Maple
Time used: 0.290 (sec). Leaf size: 243
dsolve(3*sin(t)-sin(3*t)=(cos(4*y(t))-4*cos(y(t)))*diff(y(t),t),y(t), singsol=all)
\[
y = \arctan \left (\frac {4 \cos \left (t \right )^{3}-12 c_{1} -12 \cos \left (t \right )}{6 \operatorname {RootOf}\left (36 \textit {\_Z}^{8}-72 \textit {\_Z}^{6}+16 \cos \left (t \right )^{6}-144 \textit {\_Z}^{5}-96 c_{1} \cos \left (t \right )^{3}+45 \textit {\_Z}^{4}-96 \cos \left (t \right )^{4}+216 \textit {\_Z}^{3}+144 c_{1}^{2}+288 \cos \left (t \right ) c_{1} +135 \textit {\_Z}^{2}+144 \cos \left (t \right )^{2}-72 \textit {\_Z} -144\right )^{3}-3 \operatorname {RootOf}\left (36 \textit {\_Z}^{8}-72 \textit {\_Z}^{6}+16 \cos \left (t \right )^{6}-144 \textit {\_Z}^{5}-96 c_{1} \cos \left (t \right )^{3}+45 \textit {\_Z}^{4}-96 \cos \left (t \right )^{4}+216 \textit {\_Z}^{3}+144 c_{1}^{2}+288 \cos \left (t \right ) c_{1} +135 \textit {\_Z}^{2}+144 \cos \left (t \right )^{2}-72 \textit {\_Z} -144\right )-12}, \operatorname {RootOf}\left (36 \textit {\_Z}^{8}-72 \textit {\_Z}^{6}+16 \cos \left (t \right )^{6}-144 \textit {\_Z}^{5}-96 c_{1} \cos \left (t \right )^{3}+45 \textit {\_Z}^{4}-96 \cos \left (t \right )^{4}+216 \textit {\_Z}^{3}+144 c_{1}^{2}+288 \cos \left (t \right ) c_{1} +135 \textit {\_Z}^{2}+144 \cos \left (t \right )^{2}-72 \textit {\_Z} -144\right )\right )
\]
✓ Solution by Mathematica
Time used: 0.645 (sec). Leaf size: 45
DSolve[3*Sin[t]-Sin[3*t]==(Cos[4*y[t]]-4*Cos[y[t]])*D[y[t],t],y[t],t,IncludeSingularSolutions -> True]
\[
y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}(4 \cos (K[1])-\cos (4 K[1]))dK[1]\&\right ]\left [\int _1^t-4 \sin ^3(K[2])dK[2]+c_1\right ]
\]