Internal problem ID [2871]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 122.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (\sec ^{2}\relax (x )\right ) \left (\sec ^{3}\relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.103 (sec). Leaf size: 71
dsolve(diff(y(x),x) = sec(x)^2*sec(y(x))^3,y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {3 \tan \relax (x )+3 c_{1}}{\RootOf \left (\textit {\_Z}^{6}+3 \textit {\_Z}^{4}+9 c_{1}^{2}+18 c_{1} \tan \relax (x )+9 \left (\tan ^{2}\relax (x )\right )-4\right )^{2}+2}, \RootOf \left (\textit {\_Z}^{6}+3 \textit {\_Z}^{4}+9 c_{1}^{2}+18 c_{1} \tan \relax (x )+9 \left (\tan ^{2}\relax (x )\right )-4\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.495 (sec). Leaf size: 2959
DSolve[y'[x]==Sec[x]^2 Sec[y[x]]^3,y[x],x,IncludeSingularSolutions -> True]
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