Exercise
$\frac{dy}{dx}=\frac{1-\cos^2\left(x\right)}{y\cos^2\left(x\right)}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(1-cos(x)^2)/(ycos(x)^2). Applying the trigonometric identity: 1-\cos\left(\theta \right)^2 = \sin\left(\theta \right)^2. Apply the property of the quotient of two powers with the same exponent, inversely: \frac{a^m}{b^m}=\left(\frac{a}{b}\right)^m, where m equals 2. Apply the trigonometric identity: \frac{\sin\left(\theta \right)}{\cos\left(\theta \right)}=\tan\left(\theta \right). Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality.
Solve the differential equation dy/dx=(1-cos(x)^2)/(ycos(x)^2)
Final answer to the exercise
$y=\sqrt{2\left(-x+\tan\left(x\right)+C_0\right)},\:y=-\sqrt{2\left(-x+\tan\left(x\right)+C_0\right)}$