( sin(3x) e **) + 32- – 4y = 4x (By u x2 (-1-4) (4)(3:5) dx

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: SOLVE FOR EXACT DE DIFFERENTIAL EQUATION 3. (x + 3)cos ydx - [siny In(5x + 15) - y] dy = 0

A:

Q: Solve the partial differential differential by separation of variables 70z + 6 = 0.

A:

Q: . (4x³y5 sin 3x + 3x*y5 cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A: See the solution.

Q: (1) Find the general solution for -) dx - -) dy = %3D

A:

Q: 4. Show that both x₁ (t) = et cost and x2(t) = et sint are solutions to the second-order…

A: To show that both x1t=e-t cos t, and  x2t=e-t sin tare solutions to the second‐order differential…

Q: dly dx2 - 2 dy dx -3y = COS X

A: The given differential equation is d2ydx2-2dydx-3y=cosx. We have to find the solution of the given…

Q: y' + 2xy = 0

A: y'+2xy=0

Q: Find a particular solution of the differential equation COS X dy dx 1 +ytanx = cos x e cos x for…

A:

Q: 5- = cos nx dx= [cos nx cos nx dx 0.

A: We have to solve given problem:

Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

A:

Q: 2- X. Sin (5X) dx: Cos (SX) X Sin (SX), Cos (SX) XSin (SX) XSin (SX) Cos (SX) 25 25 25

A:

Q: Since dv = cos( cos9 x) dx, integrate the differential equation to obtain the function v. V = ^p -…

A: We have to find solution

Q: 2 iii. sech x3 tanh( x3 S- -dx 1 X3

A:

Q: What is of the differential equation (3 +y+ 2y sin² æ) dx + (x + 2xy – ysin2x) dy = 0 ? O 2x sin 2x…

A:

Q: (2x-2) dx sinx dx 2. 3. √xdx 4. J² (²2x²+4x-2) dx 5. So (cosx+tanx)dx 1/1/4 6. Jo ¹/2_dx =dx √1-x²

A: Solve by integration

Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx…

A:

Q: In a differential equation where y is the dependent and x is the independent variable and the…

A: In a differential equation where y is the dependent and x is the independent variable and the…

Q: find solution of this differential equation:  y′ tanx sin2y = sin^2 x + cos^2 y

A:

Q: a particular solution that satisfies the differential equation F'(x)=3x^2 +2x -1 and the inital

A:

Q: 4- Find dy/dx for: d- y = /1+ sin³ (x5) e- y = 2(Va – 1)( f- y = cos³{sin(2x*)} x-2 x²+3x' %3D

A:

Q: /4 - x2 the integral | dx, becomes

A: Given the integrationI=∫4−x2x2dx

Q: Show that the solution of the differential equation (1–x*) = 2x(1+ y). dx 1+x given that y=1 when…

A:

Q: 2. Solve x². dy + 2xy = 4x³ using an + 2xy = 4x³ using an Integrating Factor. dx

A:

Q: Use Exact Differential method ( Rule II) to solve : (x² – y²)dy = xy dx.

A:

Q: Find dy/dx at the given point. 7x2y4=9-x2-9y  at (0,1)

A: Given: 7x2y4=9-x2-9y We have to find the dydx at (0,1)

Q: ① Solveing dy - - x dx = 。 ㅎ

A:

Q: Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete…

A:

Q: f f(x) = ex – e-x – 2x and g(x) = x – sinx, evaluate the limit of f(x)/g(x) as x approaches zero.…

A: Here we have, f(x)=ex-e-x-2x and g(x)=x-sinx We have to evaluate limx→0f(x)g(x)=?

Q: 1. x In x sec² y dy + [tan y – (In x)°]dx = 0 When:x = 1; y = "

A: The given differential equation is solved below in detail.

Q: 5. 2x sinh+ 3y cosh2) dx -- 3x cosh dy = 0

A:

Q: a differential equation is classified as a homogeneous DE if one can directly isolate all functions…

A: A differential equation is classified as a homogeneous DE if one can directly isolate all functions…

Q: obtained in factored form a linear differential equation with real constant coeffiecients that…

A:

Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

A: Since you have asked multiple questions,we will solve the first question for you . If you want any…

Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

A:

Q: Solve the differential equation by variation of parameters. ✓+y=sin²(x) - con(x) + cylin(x) + con(x)…

A:

Q: Find a result by using homogenous for (x³ - 3x²y)dx-(x3³ - y³)dy = 0

A: This question is based on solution of Homogeneous differential equation.

Q: solve using homogenous and exact. (2x-3y)dx+(2y-3x)dy=0

A:

Q: 1-f²₁ ¹/²(y² sinx dx dy) 2-√²-dxx2 0 3- f(cscx cotx)² 2 4- f₁² x (x − 3)dx for 5-S²₂ (x³ + √x) dx

A: 1.

Q: x' sin 2x dx -3x 5. X cos 2x dx

A: We solve these integral by u.v formula of integration

Q: sin 6x dx sin23x 4. 6. S Ve3x + e 4x dx ex dx 8. J 1+ e2x

A:

Q: Evaluate the integrals

A: Given integral is:

Q: 2-S S dx dy

A: to find the double integral we consider a strip parallel to x axis

Q: 2 11 y+xy+y%3D45inlnx

A:

Q: A/ By using Linear equation solve the first order differential uation y' + sec(x)y= cos(x)

A:

Q: 3. (sin'x + cosv)dx - tanxsin2ydy = 0

A:

Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

A:

Q: Obtain the particular solution. 1. 2y dx = 3x dy ; when x = 2 , y = -1 .

A:

Q: Obtain the Differential Equation from the given general solution. y = C¡ cos(4x) + Cz sin(4x) + Cx…

A: Use the following formula, to find the solution. ddxcosax=-asinaxddxsinax=acosaxddxuv=udvdx+vdudx

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.