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1.4. Solve the differential equation tx"– 2x' =0, x(1) = 7, x'(1)=6. Show transcribed image text
Use Laplace transform to solve the differential equation: tx'' + (2 - t)x' - x = 0; x(0) = 1
Use the Laplace transform to solve initial value problems 6. tx" - 2x' + tx = 0, x(0) = 0.
$4.1, Exercise 5. Solve the differential equation dt = 2x, where x(0) = 1. At what time ty will altı) = 2?
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
Solve the given differential equation. y' = 747 41
(1 point) In this problem you will solve the differential equation (+7)y"+11xy' - y=0. x" for the differential equation will converge at least on the interval (-inf.-sqrt(7)] (1) Ey analyzing the singular paints of the differential equation, we know that a series solution of the form y = . (2) Substituting y = . *" into (x2+7y" + 11xy - y = 0, you get that Multiplying the coefficients in x through the sums E Reindex the sums Finally combine...
how to solve riccati's differential equation Solve Riccati's differential equation dy +6y? = 1 (a) or (b) dy dx y(y + 2x) + 2 = 0. dx x?
Use the Laplace transform to solve initial value problems 3. tx" + 2(t-1)x' - 2x = 2, x(0) = 0.
solve each equation algebraically: a) 3+7e^2x=24 b) 2^x+5=7^3x+1 c) 3^(2x) - 3^(x) - 20=0 d) log x + log (x-5)=2 ^6 ^6 e) log(x+2)-log(x-1)=1 f) ln(log (x^2 + 2x))=0 ^3 d og, 71 Solve each of the exponenti a tions call the as well as a decimal approximation to the nearest the get the approximated solutions Yo d ac t o a) 3+72-24 d) 3 -3-20 - 0 get the approximated solution a) loe +log.-5) = 2
1. Consider the differential equation: 49) – 48 – 24+246) – 15x4+36” – 36" = 1-3a2+e+e^+2sin(2x)+cos - *cos(a). (a) Suppose that we know the characteristic polynomial of its corresponding homogeneous differential equation is P(x) = x²(12 - 3)(1? + 4) (1 - 1). Find the general solution yn of its corresponding homogeneous differential equation. (b) Give the form (don't solve it) of p, the particular solution of the nonhomogeneous differential equation 2. Find the general solution of the equation. (a)...