Solve the differential equation y't y. lny =y. et (Hint: Use the substitution u=lny)
Use the substitution
x = et
to transform the given Cauchy-Euler equation to a differential
equation with constant coefficients. (Use yp for
y
dt
and ypp for
d2y
dt2
.)
x2y'' − 3xy' + 13y = 4 + 7x
Solve the original equation by solving the new equation using
the procedure in Sections 4.3-4.5.
Use the substitution X = e' to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for- and ypp for t...
Use the substitution
x =
et
to transform the given Cauchy-Euler equation to a differential
equation with constant coefficients. (Use yp for
dy
dt
and ypp for
d2y
dt2
.)
x2y'' +
7xy' − 16y = 0
Use the substitution x = ef to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy and ypp for dt dt2 x?y" + 7xy' - 16y = 0 x Solve the original equation by solving the...
Use the substitution
x =
et
to transform the given Cauchy-Euler equation to a differential
equation with constant coefficients. (Use yp for
dy
dt
and ypp for
d2y
dt2
.)
x2y'' +
10xy' + 8y =
x2
Solve the original equation by solving the new equation using the
procedures in Sections 4.3-4.5.
y(x) =
Use the substitution x = ef to transform the given Cauchy-Euler equation to a differential equation with constant coefficients. (Use yp for dy and ypp for...
Solve the given integral equation or integro-differential equation for y(t). t y't) +27 fit-vy(v) dv=7t, y(0) =0 0
Solve the given integral equation or integro-differential equation for y(t). t y't) + f(t– vy(v) dv=4t, y(0) = 0 0 y(t) =
Solve the given integral equation or integro-differential equation for yt). t y't) + (t-vy(v) dv=51, y(0)=0 0 y(t) =
Use the change of variables to solve the differential equation. 5. xy' = y +2Vxy dy Y-3 dx y + x 7. cy' + y ln x = y lny 8. (x + yey/t) dx – xey/dy = 0, y(1) = 0)
Solve the initial value problem 2yy' + 2 = y2 + 2x with y(0) = 4. To solve this, we should use the substitution u = With this substitution, y = y' = Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. The solution to the original initial value problem is described by the following equation in x, y.
3. Solve the following differential equation: xy' +y = sin(x) +et
2. Using substitution to simplify a problem (a) Solve the following (homogeneous) differential equation using the appropriate substitution. (b) Find the solution to the equation T+3 Hint: The same substitution wil no longer work, but the equation is almost homogeneous. Use a substitution of the form r- X - h, y-Y - k to reduce this problem to the problem solved in part (a), i.e. choose h and k so that this problem becomes homogeneous in the substituted variables X...