G) (2x-yJdx + (4x. +y-3)dy=

Q: B. ty" – (t+ 1)y' +y = t?

A:

Q: Solve y"+10y'+25y=D0, y(0)=2, y'(0)=-14 y(t)=? SHOW ALL WORK

A: Given y''+10y'+25y = 0withy(0) = 2, y'(0) = -14

Q: solve using the appropriate method. (y − 1)y'= t , y(1) = −3

A:

Q: Determine if the equation (dfferential form) is exact and find the solution if it is…

A:

Q: Find the solution. 2y" - 3y' + y = 0 (A By = c,e 1- ©y = c,e Dy =c,e

A: Find roots of  characteristic  equation  of given differential equation .If roots are real and…

Q: Solve for x :C+Vz + m = A

A:

Q: solve the DE y'' - 5y' + 6y = 32xe2x, y(0) = 1, y'(0) = 0

A: *Concept:- the give differential equation is Linear differential equation of higher order with…

Q: (9x-4y+4)dx-(2x-y+1)dy=0

A:

Q: Solve the equation by determination method: Inx + ey + tanz = 3 ... (1) 2lnx + 4tanz = 5 + ey (2)…

A: lnx + ey + tanz = 3                              ...(1) 2lnx - ey + 4tanz = 5…

Q: Q1 Using a method of reduction to separable equation and reduction to linear equation, find the…

A:

Q: C. Solve for x, y, .<NOQ & M<POQ. Show complete solution. M (y – 12) (3y – 8)° (6x – 32)° P (2x –…

A:

Q: Solve the DE using the method of variation of parameters: x²y" – 4xy' + 6y =30x³, y(1) =5 , y’(1) =5

A: homogeneous system is  compare this equation with  so here we have

Q: Solve sz dz ; c:Iz-1|=1 C

A:

Q: (b) Solve 1 y +-y= 0, t> 0. t

A:

Q: 5) To find B from Mathematical equation Y = V5X + 3X +1 %3D N=Y-4Z+C? B =N X+ Y

A: Given:  Y=5X+3X+1N=Y-4Z+C2B=NX+Y To determine: The value of B from Mathematical equation.

Q: Using the variation of parameters, find the particular solution of (D2 +1)y = secx

A:

Q: dy ----- + 2xy 2x using the method for linear equations. dx Solve ww-

A: Given the ordinary differential equation dydx+2xy=2x

Q: D (ax ay +4)dxt6x= Qy=22dy=0 2).

A:

Q: Use the method of variation of parameters to solve y" – 4y +4y = 2e". %3D -

A:

Q: e2x-ydx + ey-2×dy = 0

A: e2x-ydx+ey-2xdy=0⇒e2x-y+ey-2xdydx=0Substitute  dydx with y' ⇒e2x-y+ey-2xy' =0⇒e2yy'…

Q: Find the solution to y - x+t y' = y if r(0) = 5 and y(0) = 4. %3D

A:

Q: Show that y=x?lInx solves the equation x?y"-3xy'+4y=0, x>0

A:

Q: Solve using MUC: '-8y + 16y=2(x+12) 3 y= C, e^X + C,xeAX + 8. X- 2 7 3 y=C; eX + C,xe^* + 7 X- 2 B…

A:

Q: ((x+4)(y²+1)) dx + (y (x2 + 3x + 2)) dy =

A: This separable differential equation

Q: dy 1 3x? 1. %3D xp 1+ X' 1+ X?

A:

Q: (ex-y+2=-/ -32=79 dy+52=25

A: We are asked to solve the system of equations

Q: Solve using variation of parameters y" – y = e2=

A:

Q: Use an appropriate substitution to solve the equation z15 and find the solution that satisfies y(1)…

A:

Q: Q1: using variation of parameters to solve: * y"' – 2y" – 21y' – 18y = 3 + 4e-t %3D

A:

Q: Use variation of parameters to solve the general solution 1 (D² – 3D + 2)y 1+ e¬*

A:

Q: Solve the equation ru, + (x + y)uy = 1 %3D on dof:

A: In this question, we solve the partial differential equation by using characteristic method.

Q: Solve the IVP y' = [, y+,yc0) = [2]. [et y + -1 3.

A:

Q: |2/2r| 2, dx -1

A: Let I is the value of given Integral.

Q: - y" – 2y' + 1 = (x + 1)e2x

A: Just I have used the method of variation of parameters and easily find the required solution.Final…

Q: FIND THE PARTICULAR SOLUTION: SHOW SOLUTION AND PROVE THAT THE EQUATION (y4-2xy)dx+3x2dy=0; when…

A: We have to find the solution

Q: A. y– 2y +1 = (x + 1)e²x

A: To solve the given differential equation using method of variation of parameters.

Q: B. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Repeated Roots) 2. (D4 + 6D3 +…

A: Given that: D4+6D3+9D2y=0  . Therefore, D4+6D3+9D2=0or, D2D2+6D+9=0 So, the above equation should…

Q: Solve for the particular solution: dy = y + Vr2 – y?, y(2) = 0 %3D - da

A:

Q: Solve for x and y. x + yi = 3 e2j +4e-2j

A: Given complex number - x+iy = 3e2i+4e-2i             ...........(1)We know that,eiθ = cosθ+isinθ…

Q: Solve rue I.v.P. ý + 3y'-s y = y co1=2 yco)=-3

A: Given,y(0)=2 and y'(0)=-3y''+3y'-5y=0    Integrating both sides y'+3y-5=C1...............(1)on again…

Q: Solve for the exact solutions in the interval(0, 2x). If it has no solutions, respond with DNE.…

A:

Q: Solve method of undetermined coefficients using (D+AD+8)Y 3X t, z 13e +50X when x-0, y=0, Y=D0 ゾーo

A: Given that, D2+4D+5y=13e3x+50xwhen x=0,y=0,y'=0

Q: Solve y"-xy' - By = 0, x>0 A) y = e+ B) y = c,x* + C) y= + D) y =c,3r*+

A:

Q: Obtain the general solution unless otherwise instructed a.) (9D4 + 6D3 + D2)y = 0 b.) (4D4 − 45D2…

A: (a) Consider the given equation. 9D4+6D3+D2y=0 Convert the equation into the characteristic equation…

Q: By using method of undetermined coefficient solve (D² – 3D + 2)y = ex + e2x ;D = 4 ? dx

A:

Q: B. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Repeated Roots) 4. (4D5 – 15D3 -…

A:

Q: Solve the equations by variation of parameters. y" + 2y' + y = ex

A: y''+2y'+y=ex    ------------(1) reduced equation of equation (1) is  y''+2y'+y=0    -------------(2)…

Q: ty" – (t+ 1)y' + y = t?

A:

Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y (0) = 0.4, y' (0) = –0.4, y" (0) = -0.4

A: The Symbolic form of the equation is D3+D2-2Dy  =4e-2xcos x Auxiliary  equation is D3+D2-2D=0…

Q: Solve for the values of Ay and dy if y= f(x) =x² + 2x? – 3x + 5 and x changes from 2 to 2.10.

A: Given: y=fx=x3+2x2-3x+5 And x1=2 &amp;  x2=2.10  a). We know that; ∆y=yx2-yx1 So,…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.