Show that the substitution z = sinh−1 x transforms the equation (1 + x2) d2ydx2 + x dydx = 4yinto d2ydz2 = 4y.
Question
Solution 1
Sure, let's go through this step by step.
-
First, we need to find the derivatives of x in terms of z. Given z = sinh^(-1)x, we can differentiate both sides with respect to x to get dz/dx = 1/√(1 + x^2).
-
Next, we differentiate again to find the second derivative, d^2z/dx^2. Using the quotient Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI
Similar Questions
Show that the substitution z = sinh−1 x transforms the equation (1 + x2) d2ydx2 + x dydx = 4yinto d2ydz2 = 4y.
Show that all circle of radius r are represented by the differential equation1 + dydx2 32=r d2ydx2
The roots of the following equation are approximately:x(x + 1) - x(x2 + 25 - 6x) + (x - 11)(x2 + 13x - 6) = 0Roots are not real18.8, 0.399.38, 0.8313.8, 6.83
The number of rational roots of equation x(x + 2)(x2 − 1) − 1 = 0 are/isSelect an answerA0B4C1D2
Find the gradients of the following functions:(a) f (x, y, z) = x2 + y3 + z4 .(b) f (x, y, z) = x2 y3 z4 .(c) f (x, y, z) = e x sin(y) ln(z)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.