ODE
\[ y'(x)^2=a^2-y(x)^2 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.228018 (sec), leaf count = 99
\[\left \{\left \{y(x)\to -\frac {a \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}}\right \},\left \{y(x)\to \frac {a \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}}\right \},\left \{y(x)\to -\frac {a \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}}\right \},\left \{y(x)\to \frac {a \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}}\right \}\right \}\]
Maple ✓
cpu = 0.131 (sec), leaf count = 68
\[\left [y \left (x \right ) = a, y \left (x \right ) = -a, y \left (x \right ) = -\tan \left (-x +\textit {\_C1} \right ) \sqrt {\frac {a^{2}}{\tan ^{2}\left (-x +\textit {\_C1} \right )+1}}, y \left (x \right ) = \tan \left (-x +\textit {\_C1} \right ) \sqrt {\frac {a^{2}}{\tan ^{2}\left (-x +\textit {\_C1} \right )+1}}\right ]\] Mathematica raw input
DSolve[y'[x]^2 == a^2 - y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -((a*Tan[x - C[1]])/Sqrt[Sec[x - C[1]]^2])}, {y[x] -> (a*Tan[x - C[1]])/Sqrt[Sec[x - C[1]]^2]}, {y[x] -> -((a*Tan[x + C[1]])/Sqrt[Sec[x + C[1]]^2])}, {y[x] -> (a*Tan[x + C[1]])/Sqrt[Sec[x + C[1]]^2]}}
Maple raw input
dsolve(diff(y(x),x)^2 = a^2-y(x)^2, y(x))
Maple raw output
[y(x) = a, y(x) = -a, y(x) = -tan(-x+_C1)*(a^2/(tan(-x+_C1)^2+1))^(1/2), y(x) = tan(-x+_C1)*(a^2/(tan(-x+_C1)^2+1))^(1/2)]