Solve the second order differential equation ý + ý - 6y = 8e* + 3x A:y = ce2x + cze-3x + 2e* + %3D 2 12 1 B:y = ce2x + c2e-3* + 2e* 12 2 1 C:y = ce2x + C2e-3* - 2e* -- 12 D: y = ce2x + cze-3* – 2e* ++ 12

Q: solve the differential equation of (x^3 +xy^2-2a^2)dx+(x^2y-y^3-yb^2)dy=0

A: For differential equation ,M dx+N dy=0 is tobe exact if∂M∂y=∂N∂xthen solution is∫M dx+∫ N…

Q: ven the differential equation (D3 + 9D² + 27D + 27) y = In(2x –- 3). Propose an appropriate…

A:

Q: The solution of the differential equation 3.9 + x² + x²y+ 3.9y 1+ Y dy dx using variable separable y…

A: The given equation is dydx=3.9+x2+x2y+3.9y1+y On simplifying this, we get…

Q: Solve the differential equation y" +3 y' + 2.25y = -10 e-15x %3D y(0) = 1, y'(0) = 0 by using…

A: Consider the equation:y''+3y'+2.25y=-10e-1.5xy(0)=1, y'(0)=0Consider the homogenous…

Q: The solution of a differential equation is y=c₁e4x + c₂e2x, the differential equation is given by…

A:

Q: 5). Write the first-order differential equation in standard form. (Use yp for y'.) −xy' = (8x + 7)y…

A: To find- Write the first-order differential equation in standard form. -xy' = 8x + 7y + xex…

Q: The differential equation a" + 2a - 5x = sint is equivalent to the system |a' = 5x – 2y a = y |y =…

A: To solve the system of the differential equation Differentiate  one of the equation  Now, simplify…

Q: Which one is the differential equation if its solution is y= acoSx-bsinx O a. y"-y' 0 O b. None of…

A: To find the differential equation whose solution is represented as: y=acosx−bsinx

Q: Two linearly independent solutions of the differential equation y" – 4y' + 4y = 0 are O yı = e2x, y2…

A:

Q: Solve the higher order differential equation y(3) + 4ÿ – 5ý = 0 , y(0) = 3,y(0) = -5 ÿ(0) = 9 A:y =…

A:

Q: The solution of the exact differential equation (3x² + 4xy)dx + (2x² + 2y)dy = 0 is: None of the…

A:

Q: The solution of the Ordinary Differential Equation 4y" - y' - 3y = 0 if y(0) O and y'(0) %3| 7 - is:…

A:

Q: The differential equation a" + 2a 5x sint is equivalent to the system x' = 2.x – 5y x = 5x2y - | y =…

A:

Q: 14. The solution of the differential equation: (D - 2)³y = e²x is k a) y = (₁ + C₂x)e²x + xe²x b) y…

A:

Q: Solve differential equations 1. y - xy = 0; M(1,1). - 2. y4y² = 1; M(1,0). 3. y 4. yy ry³ = 0;…

A:

Q: Given the general solution to a differential equation and its initial conditions y(x) = C, e + C,…

A: Answer and explanation is given below...

Q: 6.2 What is a differential equation, y depending on x, whose general solution is the function 21…

A: Explanation of the answer is as follows

Q: Solve the differential equation y" +3 y'+ 2.25y = -10 e-15 x y(0) = 1, y'(0) = 0 by using…

A: To solve the differential equation: y''+3y'+2.25y=−10e−1.5x where, initial conditions are y(0)=1,…

Q: Solve the differential equation (2x + y) dx - O a. 5x+10y + In |10x O b. O c. 5x O d. 5x (4x + 2y -…

A:

Q: Consider the differential equation xy - (1+ 3x)y + 3y = 0 If we know that the solution for this…

A:

Q: yp= u1e-x+ u2e2x is the particular solution proposed for the differential equation y''-y' - 2y =…

A:

Q: The differential equation, (x + 3y - 5) dx - (3x + y - 7) dy = 0 can be transformed into homogeneous…

A:

Q: Determine the solution of the differential equation у" + Зу" — 4у — 12у — 0 y = C,e2x + C,xe²x +…

A:

Q: =C2e(-2x) - 6xel-3x) - 5e (2x) + C₂e(-2x) + 6xe(-3x) + 5e (2x)

A: option A is correct answer

Q: A general solution of the differential equation - 3+4 = 0 is 1. A. y = c,e* +cze2x + c3xe²x B. y =…

A:

Q: The general solution of the given higher order differential equation of y" + 3y" - 4y =0is Oage*+…

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

Q: general solution of the differential equation xy" - 2y = Inx is O cie + cze - 2r + ; | O Cır + czr +…

A:

Q: 14. The solution of the differential equation: (D-2)³y = e2²x is k a) y = (₁ + c₂x)e²x + xe²x b) y =…

A:

Q: — 2х — 4у Find the solution to the linear system of differential equations satisfying the initial…

A:

Q: Which term is included in the solution of the differential equation y” - 2y’ - 3y = e^x , y(0) = 1,…

A: Given differential equation y” - 2y’ - 3y = e^x , y(0) = 1, y’(0) = 1

Q: The solution of the ordinary differential equation ý = y = (x + 1)e-"y² , y(0) = 7 is :Select one 1…

A: Step 1: The given differential equation is, Now integrating both sides in the above equation,…

Q: The differential equation x^2 y" - 2xy' + 2y =2x has a fundamental set of solutions (for the…

A: Concept Used:- Method of Variation of Parameters For the differential equation:…

Q: Write the first-order differential equation in standard form. (Use yp for y'.) −xy' = (8x + 7)y +…

A:

Q: The general solution of the differential equation x²y" – 2y = Inx - is O C1x² + c2x¯+ In x 1 4 -2x…

A:

Q: Solve the differential equation y' – 3y = 4et at y(0) = 6. O y = 4e3t – 2e5t %3D | O y = 4e¬3t +…

A:

Q: Solve the higher order differential equation y() + 4ỹ - 5y 0, y(0) = 3,y(0) = -5 y(0) = 9 A:y…

A: To solve the given higher order differential equation

Q: Determine the solution of the differential equation d5x -7 ds5 d*x d³x + 12 ds4 d²x + 8- = 0 ds² ds3…

A:

Q: One solution of the differential equation -y" + 7y - 12y = 0 is y = e3x. A second linearly…

A: Solution in step 2

Q: The nonlinear differential equation () - 2µ + 2h, dr dt Where u and h are nonnegative constants,…

A: Given problem is :

Q: Which one is the fourth order differential equation whose solutions are  e^(3x),e^(−3x) and  xe^(2x)…

A: We will use basic of ode.

Q: order differential equation: a. y’ = 3y + e2x           b. y’ = ___t2___           y( 1 + t3 )

A:

Q: Find the solution of the differential equation у" — 4у — 4х — Зех - y = Ce2x + C2e¯2x + e* + x а.…

A: Solution:

Q: 3- Solve the differential equation (D -9)y=3e-3 -3z a)y = cie + cze - re3z %3D b)y= ce 3 + cze3 + re…

A: For the given differential equation, First of all we find the Complementary Function (C. F.)  and…

Q: Find the general solution of the linear differential equations. (D-4D )y= 36 a. y C, + C2x+ C3e2x+…

A:

Q: The differential equation a"+2x-5x sin t is equivalent to the system Sa' = 2x – 5y x = 5x -2y y =…

A: Please refer the attached image for complete solution.

Q: 3. Find all equilibrium solutions to the differential equation y= (y+1)(y- 1)(y- 2)² and identify…

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Q: Find the solution of the differential equation y"-4y = 4x - e3x y = C,e2x + Cze=2x + e* + x a. %3D…

A:

Q: 3-  (a) solve the given differential equation  y''' - y'' -4y' +4y = 1-e^x  (b) without solving.…

A:

Q: Solve the second order differential equation ý + ý - 6y = 8e* +3x A:y = Ce2x + C2e-3x + 2e* + 2 12…

A:

Q: The general solution to the differential equation + - 2( = 0 i, Oz = C + Cze + Cze# Ot= C + Cze +…

A: topic - differential equations

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.