Can you explain why (a) a solution of r*y" + xy' + (x² – µ²)y = 0 (1) is of the form y(x) = E Anx"+r %3D n=0 (b) a solution of (1 – x²)y" – 2xy' + l(1 + 1)y = 0 (2) is of the form y(x) = Lana". %3D n=0 Can you state in few words three types of resemblance between the differ- ential equations (1) and (2).

Q: A particular solution of xảy" + xy' + (x2 −0.25)y=3x3/2sinx, x>0, Yı(x)=x−1/2sinx, yz(x)=x−1/2cosx

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Q: 10. Find the general solution of (2y) dx + (x - x'y) dy = 0. A. x*y - 2 = Cx?y B. x'y + 2 = Cx?y C.…

A: Let's find.

Q: y" – y' – 12y = -24e' where y(0) = 5, y'(0) = 3 |

A: Given differential equation y''−y'−12y=−24et where y0=5, y'0=3 We have to find the given…

Q: 2) Find the particular solution for the systen and intital values given below -35 x; X1(0) = 0,…

A: See the detailed solution below.

Q: 4. Given a system of differential equations dx = 100x - 2xy dt dy = -75y + xy dt with the initial…

A: Given dxdt=100x-2xydydt=-5y+xy with initial condition x(0)=y(0)=20

Q: x*y' + x(x + 2)y = e* %3D dy - y = x² sin x dx

A: The given equation is a differential equation, hence methods to find the type of the differential…

Q: )dx – x² dy

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Q: 1- y = %3D 2yt+1 y(1) = -2 2- y'3 =? -2xy %3D 1+r2 y(2) = -5

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: (1-x²)y" - 2xy' + (a(a + 1) + µ²/(1 − x²)) y = 0, y(0) = yo, y'(0) = y₁

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Q: Test the equation for exactness and solve the equation using Method II: (2xy – 3x?)dx + (x² + y)dy =…

A: As per bartleby guidelines we only give first question answers.

Q: 2. Find (x) which satisfies (4e y − 1)dx + e dy = 0. O p(x) = e¯² + 5e-4x O p(x) = 3e e-4x O p(x)…

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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: 8. xy +y2 - x²y' = 0

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Q: (x + 2) y' = xy + 23-3x-6, when x 0, y 1 O y = 2-e O y = 3- 2e* O y = 1+2e* O y = 3+ 2e * %3D

A: Solution of differential equations

Q: If P(x) = -1/x then the integrating factor is a. e-* 1 b. С. -x d. e-1/x

A: Consider the linear differential equation: dydx+pxy=qx The integrating factor for above linear…

Q: y== Cosinlrx) a Ca Cosla.) aSatustied if x=

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Q: Solve the initial plem - 6v + 25y = 0. v(0) = 2.

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Q: ey - x+y = 10

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Q: y" - 2y' + y = 2xe2* + 6e*, a) y(0) = 1, y'(0) = 0. %3D %3D

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Q: Show that sin(y) 2e-" sin(x)) + ( .cos(y) + 2e¬#cos(x), 2)e/ = 0 %3D is not exact but becomes exact…

A: We have to solve given problem:

Q: 3. What is the particular solution if y(1) = 0 • xy' = y+ (x² + y²) ||

A: Given:- xy' = y+(x2+y2)1/2 y(1) = 0  To find:- Particular solution of given differential equation

Q: Which of the following is a particular solution of y=et y" +2y' +y = - ? (In(t)- 2) tet (2ln(t)-1)…

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Q: Find L(y). / + 2x = 2 - x' = et (0) = x (0) = 0 -2 L (y) PL(y) = %3D s(s2 +2) 2s L (y) = %3D…

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Q: y" + 12y" + 36y' = 0, y(0) = 0, y'(0) = 1, y"(0) = -7. %3D

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Q: Determine the value of k such that y = 4x²_3e²r is a solution to x(1-x)y"+ (2x² − 1) y' + k (2x −…

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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.