Internal problem ID [14177]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-\left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime }=-3 \sin \left (t \right )+\sin \left (3 t \right )} \]
✓ Solution by Maple
Time used: 0.156 (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)
\[ y \left (t \right ) = \arctan \left (\frac {4 \cos \left (t \right )^{3}-12 c_{1} -12 \cos \left (t \right )}{6 \operatorname {RootOf}\left (36 \textit {\_Z}^{8}-72 \textit {\_Z}^{6}+16 \cos \left (t \right )^{6}-144 \textit {\_Z}^{5}-96 c_{1} \cos \left (t \right )^{3}+45 \textit {\_Z}^{4}-96 \cos \left (t \right )^{4}+216 \textit {\_Z}^{3}+144 c_{1}^{2}+288 \cos \left (t \right ) c_{1} +135 \textit {\_Z}^{2}+144 \cos \left (t \right )^{2}-72 \textit {\_Z} -144\right )^{3}-3 \operatorname {RootOf}\left (36 \textit {\_Z}^{8}-72 \textit {\_Z}^{6}+16 \cos \left (t \right )^{6}-144 \textit {\_Z}^{5}-96 c_{1} \cos \left (t \right )^{3}+45 \textit {\_Z}^{4}-96 \cos \left (t \right )^{4}+216 \textit {\_Z}^{3}+144 c_{1}^{2}+288 \cos \left (t \right ) c_{1} +135 \textit {\_Z}^{2}+144 \cos \left (t \right )^{2}-72 \textit {\_Z} -144\right )-12}, \operatorname {RootOf}\left (36 \textit {\_Z}^{8}-72 \textit {\_Z}^{6}+16 \cos \left (t \right )^{6}-144 \textit {\_Z}^{5}-96 c_{1} \cos \left (t \right )^{3}+45 \textit {\_Z}^{4}-96 \cos \left (t \right )^{4}+216 \textit {\_Z}^{3}+144 c_{1}^{2}+288 \cos \left (t \right ) c_{1} +135 \textit {\_Z}^{2}+144 \cos \left (t \right )^{2}-72 \textit {\_Z} -144\right )\right ) \]
✓ Solution by Mathematica
Time used: 60.315 (sec). Leaf size: 2033
DSolve[3*Sin[t]-Sin[3*t]==(Cos[4*y[t]]-4*Cos[y[t]])*y'[t],y[t],t,IncludeSingularSolutions -> True]
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