7yy^'cos^2(x)=sin(x)(sqrt(3y^2-pi))

解

7 y y^{^{'}} cos^{2} (x) = sin (x) (3 y^{2} - π)

y = \frac{9 sec ^{2} ( x ) + 126 c _{1} sec ( x ) + 441 c _{1}^{2} + 49 π}{7 3}, y = - \frac{9 sec ^{2} ( x ) + 126 c _{1} sec ( x ) + 441 c _{1}^{2} + 49 π}{7 3}

解答ステップ

7 y y^{'} (x) cos^{2} (x) = sin (x) (3 y^{2} - π)

分離可能 ODE を解く:

y = \frac{9 sec ^{2} ( x ) + 126 c _{1} sec ( x ) + 441 c _{1}^{2} + 49 π}{7 3}, y = - \frac{9 sec ^{2} ( x ) + 126 c _{1} sec ( x ) + 441 c _{1}^{2} + 49 π}{7 3}

y = \frac{9 sec ^{2} ( x ) + 126 c _{1} sec ( x ) + 441 c _{1}^{2} + 49 π}{7 3}, y = - \frac{9 sec ^{2} ( x ) + 126 c _{1} sec ( x ) + 441 c _{1}^{2} + 49 π}{7 3}