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First-order linear PDEs

Two independent variables instead of one, where the method of characteristics finds lines along which the equation reduces to an ODE carrying the initial data.

Notes on Diffy Qs: Differential Equations for Engineers, First-order linear PDEs

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3 exercises

Exercise 101

Solve

$-5u_x + u_t = 0$ , $u(x,0) = \frac{1}{1+x^2}$ ,
$2u_x + u_t = 0$ , $u(x,0) = \cos(x)$ .

Exercise 102

Solve $u_x+u_t+tu = 0$ , $u(x,0) = \cos(x)$ .

Exercise 103

Solve $u_x+u_t = 5$ , $u(x,0) = x$ .

Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.