Q12: What is the formula of The general solution for a D.E. with variable coefficients about ordinary point xo ?

Q: The particular solution of y+y-2y = e?x is

A: To find The particular solution of the given D.E.

Q: 7. Find the solution of the DE: (D? + 9)y = x+e2 using method of undetermined coefficients.

A:

Q: solve for y in terms of t or x, as appropriate ln y = 2t + 4

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Q: d'x +x=f(t), if x =x' = 0 for t = 0. Solve d?

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Q: Q4: Solve the initial value problem: ty = 2y +t %3D

A: The general solution is, y = y(t) = t³ + t²•C, where, C is the constant of integration.   The…

Q: x4+a* dx x3 5. S ydy Va?-y2

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Use variation of parameters to solve the general solution of the following: e2t 1. (D² – 3D + 2)y =…

A: The method of variations of parameters is a useful method when the function on the RHS of a second…

Q: Q2. If the solution of the below first order D.E is y = C ef(x,y) (x³ + xy²)y' = y3 Find the f(x,y).

A: x3+xy2y' = y3dydx=y3x3+xy2 ........................equation(1)Let put y = vx in equation(1) and…

Q: Q1:- A) solve the following D.E x + x*)»' -3y = 0 1 x?y" + В):- у" + у' — бу %3 8e3х

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Q: Q2. If the solution of the below first order D.E is y = C ef(x.y) (x³ + xy²)y' = y3 Find the f(x,…

A:

Q: Q2. If the solution of the below first order D.E is y = Cefxy) (x + xy?)y' = y3 Find the f(x, y).

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Q: Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(0) = 0 Find the general solution.

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Q: 2a |2a-a (3a-2)n dn

A: Given that, ∫02a2a-x(3a-x)xdx The  objective is to evaluate the integral. So the integral can be…

Q: Which of the following can be solved by both trapezoidal rule and Simpson's 3/8 rule? How to solve…

A: Trapezoidal Rule: For applying this rule, the number of subintervals must be a multiple of 1.…

Q: 4- Solution of the following equation 4xy²dx + (x² + 1)dy = 0 is

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Q: Q2. If the solution of the below first order D.E is y = C el(x.y) (x³ + xy²)y = y³ Find the f(x, y).

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Q: (b) Solve N +e*f + (1+x*)y = 0, %3D near x = 0, if y(0) = 1; y/(0) = 0. %3D

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Q: s.t. 0 < xị <2 0 < r2 < 2 Solve by the Frank-Wolfe algorith using xº = ( 0 0) as your initial…

A: consider the program min 12x1-52+12x2-52              ...i such that 0≤x1≤20≤x2≤2 claim- to solve…

Q: Solve the following initial values problem  y'(t)+y/2=4, y(-1)=0 y(t)=? Answer should be in terms…

A: Answer is- y(t)= 8(1-e^(-(t+1)/2)).

Q: Using the method of undetermined coefficients, write the form of the assumed particular solution for…

A: Given: y"+2y'+y=x2e-x Auxiliary equation are,  m2+2m+1=0 (m+1)2=0 m=-1,-1

Q: Q2. Apply Newton's mcthod to find the solution accurate to within 10* for the following nonlinear…

A: Using Newton Raphson method

Q: What is the general form of a particular solution that should be used when using the method of…

A: We have to find the particular form of the general solution.

Q: ,3 e s-axis is s = -t° + 12t- 45t m. elocity is zero. |

A:

Q: Q2. If the solution of the below first order D.E is y = C ef9) (+xy)y=y Find the f(x, y).

A:

Q: 2) Determine the solution to the equation y' = y + x² using the following methods a.) method of…

A:

Q: Solve the following equations for x. (a) 3e2 5e" + 2 3e2" = (3a – 1)e² + a, where a is a constant.…

A: The objective is to solve the equation for x.

Q: Given: f(x, y) = x³y – y cosh xy Solve for D132

A:

Q: Use Secant method to find to find solution accurate to within 10 for the following problem. (i).…

A: Given function is  (i) f(x)=3xex Here x0=1, x1=2 f(x0)=f(1)=3(1)e1&gt;0 f(x1)=f(2)=3(2)e2&gt;0 Since…

Q: Q5. In the given problems determine whether the given equation is exact. If exact solve. (х + у)(х —…

A: Please refer the attached image for complete solution.

Q: Q/ Solve the DEs: 1-a+ykdx+(1+x*)dy = 0

A: 1-(1+y2)dx+(1+x2)dy=0

Q: C - S N. L Solve for C: V = C - -

A: Given equation is: V=C-C-SLN We have to solve for C.

Q: (D² – 3D + 2)y = e2*(1+e2x)

A:

Q: solve the following D.E ,t<3 y" – 3y - 4y =- , y(0) = 0, y'(0) = 0 : ,t23

A: Here we will use Laplace transform method to solve the given differential equation.

Q: Use the method of variation of parameters to solve the following y + 4y + 4y e- In z, z>0

A:

Q: For the Following difpe rential equation, determine the General /Particular solutions. (1-…

A: In this question we have to find the general/particular solution of the differential equation.

Q: Q5) Solve the following using Trapezoidal rule with n=6 2 f(x) = [²xtnx. dx 0

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Q: Q2. Test for exactness and solve (4x³y3- 2xy)dx + (3x*y² – x2) dy = 0

A: Topic- solution of differential equations in exact form . Note:- as per our guideline more than one…

Q: d cSc z = -csc z cot z dz

A:

Q: Given: f(x,y) = x³y – y cosh x" Solve for D132

A: Given:                   fx,y=x3y-coshxy To find: The value of the partial derivative D132.

Q: Q2. If the solution of the below first order D.E is y = C el(x.y) (x' + xy?)y' = y³ Find the f(x,…

A: Given that The solution of th given D.E. is  y=Ce^f(x,y)

Q: If y = f(x) is the solution of æy' + 13y – axy? = 0, f(1) = 12/a, where a + 0 is a re а, number,…

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Q: Solve y' + y = f (t) with y(0) = a, where f (t) is shown on pg 577, #37 (sawtooth wave)

A: As the Laplace transform of the function f(s) is given in the question, will use Laplace transform…

Q: Q3) use Euler and modified Euler to solve and compare these values with exact solution y + 2xy? = 0…

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Q: (c) Test for exactness and solve the IVP, critically outline the particular solution (x + 5e*y)dx =…

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Q: Determine a general solution for the DE : y" + 2k?y' + k*y = 0

A: We have to find the solution for given differential equation

Q: Solve the 2nd order D.E. below using method of undetermined coefficients : y''+ 7 y' = 42 x^2 + 5x…

A: To find the solution, first, solve the homogenous ODE, y''+7y'=0 and obtain yh=C1+C2e-7x.…

Q: test for the exactness and solve the IVP, critically outlinethe particular solution. (x + 5exy)dx…

A: Given differential equation is x+5exydx-exdy=0, y0=-2

Q: Solve the following equation to obtain the family of solutions.Show your solution. (2x³-xy²-2y+3)dx…

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Q: Q3) Solve the following equation with Bernoulli equation Method, where dm 4 m³y? dy m

A:

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.