Home work #2 Methods of Applied Mathematics Solve up to 0(e*): 1) ex3 + x + 2 +€ = 0 2) y"(t) + (1 + e) y(t) = 0 ,y(0) = 0 ,y'(0) = 1 ,t > 0

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: Write the ratio as a ratio of whole numbers using fractional notation 12 to 1

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Q: e2"y + (x + y)³ = -r?.

A: Given query is to find the derivative of the expression.

Q: Solve 4 2 M-[30 Ly'. -26 -8 x (0) = -2, y(0) = 22

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Q: Use separation of variables to solved = e* (1 - y)², given y(0) = 0 Oy=-(e² - 1) + Oy=1-e-* Oy =…

A: Given differential equation dydx = ex( 1 - y )2 y( 0 ) = 0

Q: • A) Ln(y²+1)dx+ 2y (х-1) y²+1 dy = 0 B)Y = x/1-y2 dx C) xdy-ydx-x²y'dy=0 %3D 1+x2

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Q: Find all solutions to the equation: csc²(x) - 6cot(x) = -4.

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Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

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Q: If z + In(e3* - e + e²) = 0 dz find at the point (0, 0) -3 -2 3. 2.

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Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: Equating the coefficients of t" of the following equation E{{a,(z) + 2zn a, (2)]t"+1 – a', (x) t" –…

A: The objective is to obtain the relation when coefficients of tn of the following equation is equated…

Q: (a) y=In, X-4 2x+5

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: c'(x) = e(x) e'(x) = t(x) t'(x) = h(x) h'(x) = c(x) 0 1 2 1 0 4 3 3 4 1 2 لا e(x) c(x) 3 t(x) 4 1 3…

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Q: а.) Solve x' = -5] x+ -2 [sec t] x(0) 1 b.) Solve x' = x + x(0) 1 -2 U5

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Q: s to find a particular sy1, y2 of the s(x))y'+(sin(x) - cos(x)) y = e 2 = e-* cos(x)

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Q: Q.1) The general solution of the equation e' cos , is:

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Q: 3. Given the following graph and A(x)=|f(t) dt, find: A(4)= 4. y=f(t) 3 A(6)= A(10)= 6. A'(x)= "

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Q: (b) Let Y"(t) +2Y'(t) + Y(t) = 3tet, Y(0) = 4, Y'(0) = 2. Then find Y(1). %3D

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Q: Solve

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Q: Use variation of parameters to find a particular solution, given the solutions y1, Y2 of the…

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Q: Solve for the integrating factor * y (x + y) dx + (x + 2y – 1) dy = 0

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Q: a) Find a function f such that f'(x) = 4x2 – 2x – 1 and f(-1) = 2 %3D 2x b) Find the function g such…

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Q: x A(x) = † (3-1²) dt 0

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Q: (D-1)x -8y = e :+(D+1)y = te'

A: Let us consider the given system of the differential equation then to solve the system of the…

Q: Q1/ Solve the differential equation (use division method) y(x+1)dy = x(y² +1)dx

A: Division Method/Separable Method Re-arrange given differential equation such as all variables of…

Q: (b). Find a general solution to the given Cauchy-Euler equation for t > 0. t²y" - 3ty' + 3y =…

A: To Find: A general solution to the given Cauchy-Euler equation for…

Q: x² – 9 Let f (x) -. Find and simplify f' (x) and f"(x). %3D Ax2 + B f'(x) = where A = |-4 B = 54 C =…

A: Given that two function we find its first derivative and also second derivative and after find value…

Q: Solving by variation of parameter y" – 2y' + y = e* log x, the value of W(y1y2) is

A: Let's find.

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.