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 <h1>notebooks/tadeu.sagews</h1>
 <table class="header">
 <tr><td>Author</td><td>Sergio Luis Lopes Verardi</td></tr>
 <tr><td>Date</td><td>2018-06-07T17:10:39</td></tr>
 <tr><td>Project</td><td>f4457592-eb40-435e-9ca6-be9749bd8c91</td></tr>
 <tr><td>Location</td><td><a href="https:/cocalc.com/projects/f4457592-eb40-435e-9ca6-be9749bd8c91/files/notebooks/tadeu.sagews">notebooks/tadeu.sagews</a></td></tr>
 <tr><td>Original file</td><td><a href="data:application/octet-stream;base64,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" download="tadeu.sagews">tadeu.sagews</td></tr>
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<pre class="input"><code>x,a,b,c,d=var('x,a,b,c,d')</code><code>assume(a&gt;0)</code><code>assume(b&gt;0)</code><code>assume(c&gt;0)</code><code>assume(d&gt;0)</code><code>#assume((C*R^2-4*L) &gt; 0)</code><code>p=function('p')(x)</code><code>ed = ((a*x-b)^2)*diff(p,x,2)+(c*x-d)*diff(p,x,1)==1</code><code>sol=desolve(ed,p,ivar=x)</code><code>show(sol)</code><code>forget()</code></pre>
<div class="output html"><div align="center">$\displaystyle K_{2} + \int {\left(K_{1} e^{\left(\frac{b c}{a^{3} x - a^{2} b}\right)} + e^{\left(\frac{b c}{a^{3} x - a^{2} b}\right)} \int \frac{e^{\left(-\frac{b c}{a^{3} x - a^{2} b} + \frac{d}{a^{2} x - a b} + \frac{c \log\left(a x - b\right)}{a^{2}}\right)}}{a^{2} x^{2} - 2 \, a b x + b^{2}}\,{d x}\right)} e^{\left(-\frac{d}{a^{2} x - a b} - \frac{c \log\left(a x - b\right)}{a^{2}}\right)}\,{d x}$</div></div>
 
<div class="output html">Como você resolveu a EDO usando (ax+b) ao invés de (ax-b) (e analogamente para o termo envolvendo c e d), para efeitos de comparação com o Maple, deve-se considerar a solução a seguir.</div> 
<pre class="input"><code># declara variáveis simbólicas: variável independente e parâmetros</code><code>x,a,b,c,d=var('x,a,b,c,d')</code><code></code><code># impõe que todos os parâmetros são estritamente positivos</code><code>assume(a&gt;0)</code><code>assume(b&gt;0)</code><code>assume(c&gt;0)</code><code>assume(d&gt;0)</code><code></code><code># declara a função incógnita</code><code>p=function('p')(x)</code><code></code><code># define a equação diferencial</code><code>ed = ((a*x+b)^2)*diff(p,x,2)+(c*x+d)*diff(p,x,1)==1</code><code></code><code># obtém a solução da EDO e exibe</code><code>sol=desolve(ed,p,ivar=x)</code><code>show(sol)</code><code></code><code># simplifica a solução (elimina os logaritmos, essencialmente) e exibe</code><code>sol1=sol.canonicalize_radical()</code><code>show(sol1)</code><code></code><code>forget()</code></pre>
<div class="output html"><div align="center">$\displaystyle K_{2} + \int {\left(K_{1} e^{\left(\frac{d}{a^{2} x + a b}\right)} + e^{\left(\frac{d}{a^{2} x + a b}\right)} \int \frac{e^{\left(\frac{b c}{a^{3} x + a^{2} b} - \frac{d}{a^{2} x + a b} + \frac{c \log\left(a x + b\right)}{a^{2}}\right)}}{a^{2} x^{2} + 2 \, a b x + b^{2}}\,{d x}\right)} e^{\left(-\frac{b c}{a^{3} x + a^{2} b} - \frac{c \log\left(a x + b\right)}{a^{2}}\right)}\,{d x}$</div></div>
<div class="output html"><div align="center">$\displaystyle K_{2} + \int \frac{{\left(K_{1} e^{\left(\frac{d}{a^{2} x + a b}\right)} + e^{\left(\frac{d}{a^{2} x + a b}\right)} \int \frac{{\left(a x + b\right)}^{\frac{c}{a^{2}}} e^{\left(\frac{b c - a d}{a^{3} x + a^{2} b}\right)}}{a^{2} x^{2} + 2 \, a b x + b^{2}}\,{d x}\right)} e^{\left(-\frac{b c}{a^{3} x + a^{2} b}\right)}}{{\left(a x + b\right)}^{\frac{c}{a^{2}}}}\,{d x}$</div></div>
 
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