Consider the DE la. d²y = 2y = dy dx dx² Classify the DE by type (ODE/PDE and Linear/Non-Linear) and by order. 1b. Show all steps needed to verify that the function y = 5 tan(5x) is an explicit solution to the DE in problem #1a.

Q: 1. Use a suitable substitution to evaluate , (G) dx. Give you answer correct to at least 2 decimal…

A: Substitution is done for the function whose derivative is present in the numerator.

Q: dy Find using implicit differentiation. dx 2x = 5y +7y 3 %3D

A: Given:  2x3=5y2+7y Now differentating on both sides with respect to x        d2x3dx=d5y2+7ydx…

Q: Find the derivative. sin 0 d. 1 dx 1- x2 de A. tan 0 B. sec 0 C. cot0 O D. cos 0

A:

Q: explain in full detial no chatgpt, writeen out and explain thanks

A: Step 1: Step 2: Step 3: Step 4:

Q: (4) 3. Use implicit differentiation to find dy/dx of the following: x² - 5xy + y³ = 21

A: As per policy only first question is answered. Please refer to the image below

Q: Consider the following. y = (6x2 − 6x + 1)(1 + 2x) Find the value of y when x = 1. y(1) = Find dy…

A: equation of the tangent line with slope and points (x_1,y_1) is  y-y_1 = slope ( x-x_1)

Q: dy x3 + 2xy. y 7. Find for the implicitly defined function dx

A: