Find any intercepts. y5 = x3 − 49x   To find the y-intercepts, let x be zero and solve for y. y5  =  (0)3 − 49(0)          (Let x be zero.)   y5  =  0   y  =   Hence, the y-intercept is  (x, y) = (  ).

Q: ² - x ²² = y² dz ४x d²z Find the solution of xy' буду

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Q: Solve x?y" – 2ry' + 2y = x³ In x by first finding the complementary solution and then using the…

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Q: Q6. Find general solution of the DE 4x²y" + 8xy' + y = 0

A: This is Cauchy- Euler equation. We can solve this equation as follows :

Q: Find a particular solution, y,(x), of y(ª – y" = 12e3 – 5x + 2. -

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Q: Q4: Use undetermined coefficient annihilator approach to solve. y"" – 5y" + 6y' = 10x² – 5x – 6 +…

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Q: Solve second order DE  16y"-8y'+5y= 0

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Q: Find the solution to x’(t)=2x(t), x(0)=3

A: We have to solve the above differential equation.

Q: 4. For the DE y"-3y' x+3e", write the solution of the homogenous equation y., then write a…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find the solution. xy'- xy = 1- y, y(1) = 0 A y --(1 - el-) © y -1+ el+")

A: Solution of the differential equation

Q: dy = -8xy² dx 3. Solve + 4x(4x+1) y-(8.x² +4x² -1) by knowing u =x is a solution.

A: Given: dydx=-8xy2+4x4x+1y-8x3+4x2-1

Q: Determine whether y, = 3e2t – e-3t and yz = 2e-3t – 6e2t form a fundamental set of solutions. HOW…

A: We have to determine whether the given set of solutions y1 and y2 form a  fundamental set of…

Q: (a) Form the difference equation whose solution is yk = c1 + (c2+ csk)(-1)*, where c1, cz and cs are…

A: Given that the solution is yk=c1+c2+c3k-1k. To find the difference equation of this solution: For,…

Q: Verify that y, = e2x and y2 = e5×are solutions of у" - 7у' + 10у %3D 0

A: We have to verify that the functions y1=e2x and y2=e5x are solutions to the given differential…

Q: Solve second order DE y" - 4y' + 4 = 0

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Q: Use undetermined coefficients to find the particular solution to y'' - y = 4e t Y(t) =

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Q: Solve * + 3x - 4x = 20t, given that at t = 0,x = 0 and i = 0.

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Q: Find the general solution of (xy² + x²)dy + a. 3xy + y3 = C b. 3xy - y3 = C xydx = 0 с. -Зху - уз с…

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Q: 3. Find the number of non negative solutions to x +y + z + w = 21.

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Q: z = xy dy x2+y= 2x/1-x’y² dx 2. Using the substitution ,change the to a separable equation. Hence…

A: We are given the differential equation  xdydx+y=2x1-x2y2 we have to use the substitution z=xy.

Q: Find the general solution to y" – y' – 2y = 3x + 4. (Be sure to find the values of the coefficients…

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Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 %3D

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Q: Solve for y, where y is a real number. V6y-2 /9y-8 If there is more than one solution, separate th…

A: We know that  If  √(x+a) = √(b+c) Then squaring both sides x+a = b+c Then we find x x = b+c-a

Q: Solve the DE: (2-x) y³ +(2x-3) y'' - xy' + y = 0, x<2, given that y(x) = ex is a solution of the…

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Q: Q3. Solve for t ex* e2x+1 = et

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Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 x2 а у 2e + 2 - ex2 b. y =+…

A: The given differential equation is:y'=x3-2xywhich can be written asdydx+2xy=x3which is a first order…

Q: x1 and x2 are the solutions for x²+2020x+1=0 y1 and ye are the solutions for y²+2021y+1=0 find the…

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Q: Solve for x and y 3x +2y=16 7x + y = 19

A: Answer is- x=2,y=5 Explanation is given below...

Q: Find the particular solution: y" + 16y' = 0, when x = 0, y = 0, y' = 0, y" = 1

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Q: 7. Verify that y = x2 - 1 is a solution of (y')* + y? = -1.

A: Given- y=x2-1 To verify- That the above function is the solution of y'4+y2=-1.

Q: Solve (1- x2)y" +2xy'-2y = 0 on (-1,1) given that y1 = x is a solution.

A: Let us consider the given differential equation P(x) y''+Q(x)y'+R(x)y=0 Then the solution of the…

Q: Find the general solution to y′′+4y′=0. Give your answer as y=... In your answer, use c1 and c2 to…

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Q: =). Solve the equation zxx = x² + xy² when x = 0, z, = y³ and when x 2, z = y. %3D

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Q: a. Obtain the general solution of the following i. (4+x)y'= y³

A: Solve the differential equation using variable separable method. According to Bartleby answering…

Q: Find the particular solution y''-2y'-3y=0; when x=0, y=0, y'=-4

A: It is given that the differential equation  y''-2y'-3y=0,  y0=0 and y'(0)=-4     The given…

Q: Find the solution of: y'' - y = 56e^(3t) With y(0) = 9 and y'(0) = 6. y =

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Q: 2x2y'' + 3xy' - y = 0 , x>0   y1(x)= x1/2 and y2(x)=x-1 Please verify that I have solution.

A: Differential equation.

Q: 4. Solve for x. MZWYX = 56x +1 M2WLX = 58x - 1 4. Solve for x Y

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Q: Solve the equation for x if 0 < x < 2pi 8sin2x+8cosx−10=0

A: Given, 8sin2x+8cosx−10=0                            0 &lt; x &lt; 2π 8(1- cos2x) + 8cosx−10 = 0…

Q: Use the method of undetermined coefficients to determine the form of a particular solution for the…

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Q: 5. Solve the equation y-y'y"=1, given that y=√2 and y'- and y'= when r=0.

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Q: Use Gauss-Seidel method to solve for the value of x, y and z. 5x' + In 2y - 4/3z = 51.2118 2x - 5 In…

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Q: 4. Find the constant a so that Ø(x) = xe2x is a solution to y' + ay – e2x = 0 А. 4 В. 1 C. -1 D. -2

A: We have to find a

Q: b- Find the solution of f(x) e-x, let x, 0 and E- 10-5

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Q: Use the method of reduction of order to find a second solution to ty" - (4t – 4)y' + (4t – 8)y = 0,…

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Q: Find the particular solution of (2x + 3)y = y + (2x + 3)/2; when x = -1, y = 0 Show your solutions…

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Q: Find the general solution of: x² = y² QY_ dr

A: We have to find general solution of given differential equation.

Q: Solve for y. P(0)=(-12/37, y), P(0) is in Ql

A: Given P(θ)=-1237, y and P(θ) is in Quadrant 2.

Q: Find the solution such that y' = 2(2x – y) passes through the point (0, -1).

A: From the given differential equation: y'=22x-y So, we can also write as: dydx=4x-2y....(1) Now use…

Q: Use undetermined coefficients to find the particular solution to y'' + y' - 20y 20ye 4¹(-3 + 24x)…

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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.