Errors in the First Edition of
Handbook of Differential Equations

LAST UPDATED: April 21, 1998

NOTE THAT THERE MAY EXIST ADDITIONAL ERRORS IN THIS EDITION. PLEASE LOOK AT THE LIST OF ERRATA FOR LATER EDITIONS.

1.

On page 288, equation (75.1) is $$y(x)=\frac{w'(x)}{w(x)} \frac{1}{a(x)}$$. This is incorrect, it should have been (note the minus sign) $$y(x)= - \frac{w'(x)}{w(x)} \frac{1}{a(x)}$$

2.

On page 289, equation (75.5) is $$y(x)=\frac{w'(x)}{w(x)} e^{-x}$$. This is incorrect, it should have been (note the minus sign) $$y(x)= - \frac{w'(x)}{w(x)} e^{-x}$$

3.

On page 376 the worked example uses the equation $$\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial z}+\frac{u}{2t} = \nu\frac{\partial^{2} u}{\partial {z}^{2}}$$. This equation is not solvable by similarity methods. The second edition used, as an example, the equation, $$\frac{\partial u}{\partial t}+\frac{u}{2t}=\nu\frac{\partial^{2} u}{\partial {z}^{2}}$$.

4.

On page 577, equations (163.8) and (163.9) are

$$\begin{split} k_1 &= h g\left( x_0,y_0, v_0 \right), \\ k_2 &= ... ..._3, v_0+ \phantom{\frac12} k_3 \right), \\ \end{split}\tag{163.8}$$

and

$$\begin{split} y(x_0+h) &= y_0+ h v_0+ \frac16 \left( k_1+k_2+k_... ...frac16 \left( k_1+2k_2+2k_3+k_4 \right). \\ \end{split}\tag{163.9}$$

They are incorrect, they should have been (note the second term in the defining equation for k₃ , and the lack of an h in the equation for y(x₀+h) ):

$$\begin{split} k_1 &= h g\left( x_0,y_0, v_0 \right), \\ k_2 &= ... ..._3, v_0+ \phantom{\frac12} k_3 \right), \\ \end{split}\tag{163.8}$$

and

$$\begin{split} y(x_0+h) &= y_0+ h v_0+ \frac16 h\left( k_1+k_2+k... ...frac16 \left( k_1+2k_2+2k_3+k_4 \right). \\ \end{split}\tag{163.9}$$