Check that each of the following functions solves the corresponding differential equation, by computing both the...

Check that each of the following functions solves the corresponding differential equation, by computing both the left-hand side and right-hand side of the differential equation

A) y=tan(x) solves dy/dx =y^2 / sin^2 (x)

B) y=x^2 +5x solves (x)dy/dx= y+x^2

C)y= 1/ C+x^2 solves dy/dx= -2xy^2

D) y= xln(x) solves (x) dy/dx = x+y

Solutions

Expert Solution

We check the solution of the given differential equation by using differentiation.

milcah answered 2 years ago

Next > < Previous

Related Solutions

Check that the following differential equation is not exact. Find an integrating factor that makes it...

Check that the following differential equation is not exact. Find an integrating factor that makes it exact and solve it. ydx + (3 + 3x-y) dy = 0 __ Solve the initial value problem: (cos xsen x-xy ^ 2) dx + (1-x ^ 2) ydy = 0 if y (0) = 2 __ Solve the initial value problem: y ^ (2) cosx dx + (4 + 5ysenx) dy = 0; y (π / 2) = 1

Verify that the indicated family of functions is a solution of the given differential equation. Assume...

Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution. d^2y/ dx^2 − 6 dy/dx + 9y = 0; y = c1e3x + c2xe3x When y = c1e3x + c2xe3x, dy dx = d2y dx2 = . Thus, in terms of x, d^2y/dx^2− 6 dy/dx + 9y = + 9(c1e3x + c2xe3x) = . 2) In this problem, y = c1ex + c2e−x is a two-parameter family...

Write a full program that solves the following equation and displays the value for x and...

Write a full program that solves the following equation and displays the value for x and y: 3.4x+50.2y=44.5 2.1x+.55y=5.9

In Exercises 1-38, solve each differential equation using variation of parameters. If an equation can be...

In Exercises 1-38, solve each differential equation using variation of parameters. If an equation can be solved using undetermined coefficients, do so. If both methods can be used to find Yp, which method is easier when both can be used? y"+2y'+50y=e^(-t)csc(7t)

Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...

Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by means of a power series about the given point x0. Find the recurrence relation; also find the first four terms in each of two linearly independent solutions (unless the series terminates sooner). If possible, find the general term in each solution. (1-x)y"+xy-y=0, x0=0

Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...

Solve the following problems. a) What is the order of the differential equation ? ′ =...

Solve the following problems. a) What is the order of the differential equation ? ′ = ? 2 − 3? − 10? Is it linear ? b) Determine whether the differential equation ? ′ = ? 2 − 3? − 10 possesses constant solutions. If yes find these constant solutions. c) Find the value(s) of ? so that the function ? = ? ?? is a solution of ? ′′ − 3? ′ − 10? = 0. Do you think...

Question 3: Exact Differential Equation i. Test to see if the following equation is exact, if...

Question 3: Exact Differential Equation i. Test to see if the following equation is exact, if exact solve for the general solution (??/??) +(2? ????+?^3?^?)/(?^2cos?+3?^2?^?)=0 ii. Solve (?+????)??+(?????−2?)??=0 iii. Solve (?^2+?)??+(?^?−?)??=0 iv. (2?−3?)??+(2?−3?)??=0 I am sorry I could not send a photo. Whenever I try from the app it posts another question on the same page. I tried doing them individually and the only thing that happened was that the same question got posted 4 times. I would appreciate your...

For the differential equation dy/dx=ye^x check all that apply A. PDE B. ODE C. homogeneous D....

For the differential equation dy/dx=ye^x check all that apply A. PDE B. ODE C. homogeneous D. linear E. constant coefficients F. autonomous G. system this is a differential equation problem. i was thinking it was A,C,F but thats not correct. any suggestions would help.

For each problem (A and B), - Seek power series solutions of the given differential equation...

For each problem (A and B), - Seek power series solutions of the given differential equation about the given point x0 and find the recurrence relation. - Find the first four terms in each of two solutions y1 and y2 (unless the series terminates sooner). - By evaluating the Wronskian W(y1, y2)(x0), show that y1 and y2 form a fundamental set of solutions. - If possible, find the general term in each solution. A) (1 - x)y" + y =...

Subjects