The general solution of the differential equation $\sec^2x \tan y \,dx + \sec^2y \tan x \,dy = 0$ is $\sec x \sec y = k$ $\sec x \tan x + \sec y \tan y = k$ $\sec x \tan y = k$ $\tan x \tan y = k$ None of the above
Added by Trevor H.
Close
Step 1
Then, we have: $\frac{dv}{du} = -\frac{(1+u^2)v}{(1+v^2)u}$ This is a homogeneous differential equation. We can use the substitution $v = u \cdot w$ to solve it: $\frac{d(uw)}{du} = -\frac{(1+u^2)(uw)}{(1+(uw)^2)u}$ Now, we can simplify and separate the Show more…
Show all steps
Your feedback will help us improve your experience
Gregory Higby and 63 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Solution of the differential equation $\cos x d y=y(\sin x-y) d x, 0<x<\frac{\pi}{2}$, is (a) $\sec x=(\tan x+C) y$ (b) $y \sec x=\tan x+C$ (c) $y \tan x=\sec x+C$ (d) $\tan x=(\sec x+C) y$
Find the general solution of each of the differential equations in exercise. $$ \frac{d^{2} y}{d x^{2}}+y=\tan x \sec x $$.
Explicit Methods of Solving Higher-Order Linear Differential Equations
Variation of Parameters
Solve each differential equation. $$y^{\prime}+y \tan x=\sec x$$
Transcendental Functions
First-Order Linear Differential Equations
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD